Your April time frame might be perfect to see the Death Valley wildflowers depending on winter moisture. Some years are incredible! We live in Pahrump and visit the park often twice a week in fall, winter, and spring... not so much so this time of year.
Keep in mind the park is HUGE! There are over 300 miles of paved roads, and several hundred back country roads and trails. If you aren't taking your own 4x4 vehicle, I'd suggest renting a Jeep. The real interest of Death Valley to us is in the mountains that surround the valley.
Here is a link to a short DVNP 4x4 route video I made a couple years ago. It snowed in the mountains and was darn chilly at 3000 ft...
Off Pavement's Death Valley - Rhyolite and Titus Canyon
