Ahhhh! Death Valley! One of our favorite destinations... There's so much to see there that you could spend a month and not see a fraction of what's there. OTOH; depending on what you like to see (if it takes entertainment and flashing lights), you'll be hard pressed to spend more than a night. Fortunately, Las Vegas isn't far...
If by chance the winter has brought rain, Death Valley is truly an enchanted place to visit. April in Death Valley is probably one of the best times to be on this earth. If the spring was wet ( a half inch or more of rainfall), you can rest assured that the valley floor and walls will be covered with wildflowers. There will be flowers from the size of pin holes, within 2 millimeters of the ground, to Desert Sunflowers over 6 feet tall. If you've never experienced the desert in bloom, there's no way it can be described using only words. It is a sight to behold at least once in your life. There are few places in the world where one can see 100+ miles, and find every inch of it painted by flowers. Each hillside, having different elevations, exposures, and soils will present a different color as the flower that flourishes in that localized microclimate adds to the overall display. Bring lots of film, and wide-angle lenses. Here, although it's near but not in Death Valley, is an example of WildFlowers!
Avg. temp there during the day in February-March is typically in the mid to upper 70's for the daily high, and mid 40's for night time low. In April daytime temps will typically get to the 90's, with days to 100F+ sprinkled in. At night it should cool off into the 60's to low 70's. The dry air makes the heat bearable. But it's still dangerous. So take some care. In mid-summer, it can be a month or more before the night time temps drop below 100F.
Depending on your needs (if you're prepared to dry camp), I'd go against some of the other advice I've heard and not recommend Furnace Creek or Stove-pipe Wells. Too commercial and populous (unless that's your cookie). I'd suggest you drive up (North from Furnace Creek) to Mesquite Springs. It's just south of the North-end entrance station, on the west side of the road. It's kinda remote, and even in the season, it's not usually full. We like it. Obviously; YMMV. Ideally, you should have a toad; high-clearance and/or 4X4 recommended.
From there you can day-trip up to Ubehebe Crater. An enormous volcanic cauldera blasted out by water leakage getting to the hot magma below. If you're so inclined (you're physically fit enough) the walk down into the crater and back is tough but exhilarating. Or you can walk around the top of the crater visiting it and the Little Ubehebe Craters nearby. From that same area, you can tap any of hundreds of miles of back (dirt) roads. You could go to the "racetrack" (the place where stones mysteriously move (due to frost-thaw cycles, not faeries)), Teakettle Junction, or go on through to Saline Valley. We spent two nights near Teakettle Junction when that Hale-Bopp comet was making it's appearance. In San Jose, you could cover the comet with your thumb at arms length. Out there, a couple of hundred miles from any city lights, at 4,000 ft in the dry desert air, Hale-Bopp covered more than 2/3'rds of the visible sky. No way you could cover it with a newspaper at arms length. You can also pop up to Scotty's Castle for a peek. It's kinda neat. If you want to eat out, the drive to Beatty (if you have a toad) is not that long. Food in Nevada is cheap, as is gas and lodging.
As you work your way south in Death Valley, you should be able to see many different kinds of flora and fauna. Despite being so harsh, the beauty of this landscape is overwhelming. At that time of year, you should look for Flycatchers hawking bugs. You should be able to find; Western, Cassin's, and possibly vagrant Eastern Kingbirds; Black and Say's Phoebes; Black-chinned, Costa's, Calliope, and Broad-tailed Hummingbirds; Vermillion, Ash-throated and Gray Flycatchers; and other birds too. Watch for dark morph Red-tailed Hawks, Chihuahua Ravens, Golden Eagles, and owls and bats at night too. The desert is alive in ways you'd never suspect.
Be sure to stop at the Sand Dunes just short of Stove-pipe Wells. Take the time to walk out to them. They're breathtaking. The restaurant at Stove-pipe Wells is fine, perhaps only a little pricey. A few hundred meters west of Stove-pipe Wells is a road up to Marble Canyon. Drive up and take the walk along the canyon. You'll see amazing rock and geologic formations. You should be able to see roosting bats, the birds I'd already mentioned, and lots of swallows and swifts. If you're looking for a "Mickey D's", you're outta luck going up there...(:-)!
Continue west on up the hill heading towards Panamint Junction. About 5 or 6 miles you'll find a left turn (South) along the emigrant canyon trail. This road will take you to Wildrose Canyon (if they've fixed the road yet--inquire locally, and/or observe the signs). There are both mines and ghost town ruins along both sides of the road. Some of the mines are open. Bring flashlights and self-guide yourself along those that you can enter. As you crest Immigrant Pass, you'll descend into short valley just before you get to the Wildrose Canyon itself. The campgrounds are primitive, but free. You can continue up that road to the old charcoal kilns. Kinda neat to crawl around in. Continue on up the road to Telescope peak. There are camp grounds up there, but I think they're tent only. Things have been changing there, so you should inquire locally. One of the best things about driving from the valley floor up to the peak is that you're traversing seasons from deep summer at the bottom, to alpine spring at the top. There's snow up there year round. If the valley floor is too uncomfortable and hot, move up! You'll probably be able to find a level that's just right. In addition to that, as I'd indicated earlier, the wildflowers are subject to microclimatic influences. As you move up, you'll be stepping back through time (as blooming goes) and be able to enjoy the entire spring -> summer convergence all over again...
When you're done up there, drive back down into the valley. You could escape out the Wildrose Canyon road. But I understand that they're not maintaining it any more (they want it to go away). In my Land Cruiser, it's no problem. And I know that a few years ago my (very low ground clearance) 500 SL made it just fine too. But conditions vary. So inquire. Unless you're leaving, don't head west. You don't really want to get out of the park, and it'll just cost you a lot of fuel to climb those hills back in again. Instead, return and go towards Furnace Creek. Along the way, stop at the Salt Creek Interpretive trail. It'll take you to a stream that has a tiny pup-fish native only to Death Valley. How they survive in that heat is a miracle in itself. Stop at Mustard Canyon, and take that loop. Stop at the Borax works. An interesting place steeped in history.
The next place you'll find is Furnace Creek. If you fly, you can fly in. But be sure to watch your pressure altitude when you leave. You might be below sea-level, but you'll find that your charts probably don't go all the way to 125F! There's a pretty nice golf course there too, as well as camping and rooms too. I find the camping down there too spare and open. But in April, it should be okay. If it was me, I'd stay up at Mesquite Springs, and do the rest of these points of interest as day-trip loops. For a change of venue, there are several places to eat at Furnace Creek, and a little store. If you can spring the bucks, spend a night at the Furnace Creek Inn. Pricey, but wonderful turn-of-the-last-century type accommodations and hospitality. They've got an excellent restaurant at the Inn (not the ranch--that one's just okay), and a long and well stocked wine cellar. We spent a week there doing a cooperative vertical wine tasting put on by Dry Creek Vineyards. Great stuff! One of the nice things is that the Inn gets its water from the Travertine Springs a few miles east on 190 towards Death Valley Junction (which is outside the park). The "cold" water is lukewarm all the time just as it comes out of the ground. A lukewarm "cold" shower after a day tromping around in the desert feels heavenly!
Just past the Furnace Creek Ranch area (but before the Inn), you'll come to a right (South) turn. Take it. Drive south along this road (sorry, I'm doing this from memory, and I don't recall the road name or number...) take the time to drive a few miles south and visit Artists Drive. It's a loop on the east side of the road--I recommend visiting it on a clear day, later in the afternoon. At that time the sun will be at its best illuminating the minerals and geology in that incredible canyon... Continue on and drive out to, and then walk out onto, "The Devils Golf Course". On a calm day, if you'll sit still and wait until there's no other extraneous noise, you'll be able to hear a very faint tinkling sounds. This is caused by millions of crystals growing, bumping into each other, and shattering. But I like the Indian legend better. They said it was spirits talking... This happens constantly when conditions are right--and you're in the right frame of mind. It's more than just a little eerie! You need to do this in the hottest part of the day when there's little or no actual breeze (natural convection is all that's required). Next, stop at Bad Water (just below Dante's View). Go past the tourist stop, and pull over a 1/4-1/2 mile or so further south. Walk out onto the salt lake. This lake is several thousand feet deep. But so filled with salts and chemicals that its surface is damp, but otherwise solid. Nothing can live out there. While there may be some mushy sections around the edges, just slog through them and you'll eventually find yourself out in the salt. We usually try to walk out about half-way to the other side. It's neat in that no one else will usually do it. It's best to do that at mid-day too. But be sure to have a hat, sunglasses, sunscreen, and water!
At this point, you can continue on and eat or get gas about 40 miles further over Jubilee Pass at Shoshone, or you can go on only about 20 miles and take the West Side Road. A right turn, it will take you back north "up" the valley, but on the opposite side. This road will join up to the road you were on, and will take you back to highway 190 to Death Valley Junction. Although okay for most vehicles, it's dirt and rough. So drive slow...
When you get back to paved road, turn LEFT (North), towards the Inn. Turn RIGHT (East) at 190, proceed east, past the Inn. If you have the requisite high clearance 4-wheel drive vehicle you might indulge yourself with a drive up Echo Canyon to the Inyo mine. A neat and well preserved mining town. Lots of fun to wander around in. But stay clear of the various shafts and pits. You can die up there!
Plan to stop at Zabriski Point. Late afternoon is best there too. With a low sun angle, all of the chocolate brown mud hills form an awe inspiring physical relief painting. It's just beautiful! There's also a trail that runs from there down to and through Golden Canyon. A great daytime (early morning) hike if it's not too hot. We would stay at the Inn. After breakfast we would walk up to Zabriski Point, down Golden Canyon, and back to the Inn for cold brewski's with lunch. Then we'd reverse that course, and come back for dinner. It made for a long and exhausting day. With hundreds of short to long mines and other diggings along the way, you never get bored...
If you continue east, take a right turn onto "20 Mule-team Drive". It's short and easy enough for most any vehicle. Next you might consider taking a left turn and visiting the "Hole-in-Wall" side road. Drive out to the Red Amphitheater area. You'll experience the desolation of the desert just fine there...
Continue east, turn RIGHT (South) on the road marked for Dante's View. It's a climb, and you'll go from near sea-level to over a mile up. At the top, you can walk out and look down on Badwater a mile below. The people out there will look like bugs. They'll be the only "bug-like" things you'll probably find. It's so dry, windy, and harsh up there, that you could stand there naked, and nothing would bite you--except the sun (unless you've brought some rowdy guests...)! During your trip up, you'll again be able to see the progression from summer plants to spring wildflowers. Depending on how wet the preceding winter was, it can be anywhere from a yawner to a stunner (if you like to observe beautiful flowers and scenery, that is...).
Continue on 190, until you get to the Amergosa Opera house. I don't know if it's still active, but there used to be a 70+ year old woman who puts on a ballet show most evenings at an old gold rush era theater she reconditioned. Well worth the visit.
From there, you might want to head north on Nevada 127 to Beatty. Lots of places to stay and eat, and get gas. If you're still working out of Mesquite Springs, you can return there via Nevada 374. If you can work it (and have a high clearance vehicle), you might stay in Beatty for the night. And then return to Mesquite Springs via 374 and Titus Canyon. A marvelous ONE WAY downhill tour de force through more geologic history and beauty then they ever taught you in any school. Past the ghost towns of Rhyolite and Leadfield. In the canyon you can find the Desert Orchid which grows nowhere else in the world, petroglyphs, Desert Bighorn, a sweet water spring, and lots of desert solitude and beauty (we MTB this nearly every year--great ride!).
If you still have time, you might consider an off-road excursion north of Death Valley to the Saline Valley via Eureka Sand Dunes National Monument. Some of the largest sand dunes in the world can be found there. And usually, there's no other human begins within 100 miles...
There are thousands of miles of dirt road, and hiking trails out there. Hundreds of old ghost towns and mines. Dozens of peaks, valleys, and canyons. You could spend a lifetime out there getting to know that place. But never forget, it's a dangerous place. Always carry water and let someone else know where you're going, and when you'll be back.
Y'all enjoy. Y'hear?