Never been to Rhyolite, but as far as photography goes, in Death Valley it's not so much where to go, it's when. Early morning and late afternoon are the times of day when you'll get the most dramatic lighting.

My favorite website containing the most current and detailed Death Valley info is this:
http://www.ridgecrest.ca.us/~matmus/DeathV.html

If it were me, I'd probably try to visit the park south-to-north as the day progresses. Titus Canyon is absolutely spectacular in the late afternoon. It's a shame that it's still closed (just checked the DV "morning report"). If it happens to open prior to your trip, it's worth a visit. It's too bad Hwy190 is closed, since you'll either have to drive in and out via Hwy95 through Beatty, which makes for a helluvalot of repeat driving, or via the southern entrance (Hwy178) via Shoshone, but if you get an early start, you should have plenty of time to make it up to Badwater before it gets too hot. Then check out Devils Golf Course, Artist's Palette (closed to vehicles, but apparently not to pedestrians; Bummer! it would be a long hike, especially if it's hot!), and the other sites along the road as you approach Furnace Creek. Stop for a snack or lunch at Furnace Creek, and watch a quick video presentation about DVNP at the visitor center. In the afternoon, you can continue north to see or play on the sand dunes near Stovepipe Wells, and then go drive Titus Canyon to experience dramatic shadows cast by the late afternoon sun. If Titus Canyon isn't open, another really neat place to check out is the Chloride Cliffs, just south of Daylight Pass on Hwy 374. Accessing the Chloride Cliffs may involve a bit of moderate 4-wheeling and some trailfinding skills, but if you consult a topo map at the visitor center first, you should be fine and will be afforded excellent views of the valley below.

Here are some pics I took on a trip to Death Valley in 1999:
Click me (please excuse the relatively poor image quality- they are scans of 35mm prints)