"January will have a lot of people in Anza - not crowded, but you'll never feel alone"
Haha, for somebody coming from the East Coast, I'm not quite sure that's entirely true ;).
The whole place is cool with a lot of camping anywhere. I personally like Jasper Trail as one of the first places to camp. Fish Creek is a cool place, but there'll be more people there - but it's undeniably cool (in a State Park, not National Park, kinda way). Nearby Valley of the Moon has really cool camping too, but it's on the Mexican border, so you'd have to be comfortable with that.
Coming from Las Vegas, you might also consider doing the Mojave Road - I personally love that place and the landscape is quite varied. It's a good three-day trip end-to-end if you want to get the most of it.
A somewhat different place to consider (but on the way) would be Idyllwild / Thomas Mountain area. It's going to be weather dependent, but a lot of really great camping around there (it's mountainous with trees and granite, so not the desert experience).
Oh, and finally - solo is totally fine - I do that all the time and as long as you're staying off the trails rated hard, you'll be totally fine in the Taco. The winch isn't of much use anyway, since there isn't a tree in sight... (unless you do Idyllwild / TM).