The main roads in Death Valley are fine. Hwy 190 is a state highway. Badwater Road, Beatty Cutoff, Mud Canyon, Daylight Pass, and North Highway (aka Castle Road) are all paved. Emigrant-Wildrose Road is paved except for a 3-mile stretch that is graded gravel, regularly maintained and safe for any car driven carefully.
Some of the natural wonders are on graded gravel roads that can be rough, but are safe if you take it easy (mainly to protect your tires). Those include Mosaic Canyon, Salt Creek, Devil's Golf Course, Natural Bridge, and the west end of Titus Canyon.
A convertible would be a fun way to go if the wet weather stays in the Bay Area!
Edited: 10:20 pm, November 20, 2012