What type of vehicle will you be driving? That will make a big difference on which mountain you decide on.
I wander around in the desert this time of year. You might want to pick up Andy Zdon's "Desert Summits" book as it is a good basic resource.
I have some photos and maps online of desert peaks I've visited - I don't have them all that well organized; so I'm not sure how much help they will be:
http://kathywing.smugmug.com/CaliforniaHikesandScrambles/California-Desert-Hikes-andSome of the Southern California desert peaks that allow you to park just off paved roads if you are driving a low clearance passenger car:
Pyramid Peak in Death Valley
Corkscrew Peak in Death Valley
Stewart Point in the Resting Spring Range near Shoshone
Pahrump Point in the Nopah Ranch near Shoshone
Eagle Mountain north of Shoshone
Rosa Point in the Santa Rosas (Anza-Borrego Area)
Villager and Rabbit Peaks in the Santa Rosas (Anza-Borrego Area)
Sheep and Martinez Peaks in the Santa Rosas (Access via Cactus Springs Trail off SR74
Spectre Point in the Coxcombs - Joshua Tree NP
Sheephole Mountain in the Mojave near Twentynine Palms
Towne Peak and Panamint Butte (done together starting at Towne Pass)in Death Valley
It is possible to run into a bit of snow on some of these peaks in the winter, but not usually enough cause any problems.