By all means, check the NPS Death Valley site (
http://www.nps.gov/deva/index.htm) for current conditions, as previously suggested. You'll also find a wealth of information on the site, and can print it and take it along. Among that info is an excellent map of the park (
Dead Link Removed) that is very handy to print - particularly if you have a large printer. Note that spring comes early in DV, and it's often already pretty toasty by April or May.
You'll also want to check with the park staff at the Visitor's Center once you arrive for more detailed info about current conditions, road closures, etc. Paying attention to the current weather in the area (not just that in the immediate valley) is essential. Staffing at the park has been reduced in recent years, so you can't always depend on the park rangers to be patrolling all areas of the park on a regular basis. Dirt roads (like the West Side Road) are only graded every couple of years, so they are often deeply rutted, and slow going at the best of times.
Be sure to include the Emigrant Canyon Road on your itenerary. There is interesting geography along the road (distinctly different that that of the Valley), and some interesting sites including the Charcoal Kilns (the Bee Hives). Note that there is nothing left of the Skidoo townsite beyond rusted cans, so you may not find the trip up that (somewhat harrowing) road to be worth the effort.
I also found the Keene Wonder Mine, off the Beatty Cutoff, interesting. The side road is long (and rough) enough to discourage too many tourists from getting in your way.