Good idea spending some time close to Fresno to make sure all the bugs are worked out before getting too far away. Highly recommend Merced River Recreation Area at Briceberg off Hwy-140 provided the gravel road is open to the campsites. Also note that there have been several forest fires and the highway itself may or may not be open due to slides and what not. Always best to check:
There is a beach site camp at the first area and an isolated spot at the next area. Many of the sites are walk in types but during winter you can usually find a vehicle camp during a weekday. The last groups of camps have several sites that are situated close to each other. It's low enough to avoid snow and very nice at that time of year. No power or water but vaulted heads. The drive into the park isn't that far. El Portal has a nice little store and fuel is also available (at a high price).
In the park itself prepare to install chains at this time of year. Even with a 4x4 they may ask to see your set of chains. I've never had an issue finding a camp in the valley during winter provided it's not around a holiday or the super bowl. However the park tries to jam everybody together so you might have close neighbors. Still beautiful though. Bears don't always hibernate in the valley so camp as if it's summer.
Further south there are several spots open around the lower Sierra scenic byway and around Bass Lake. Some at Bass lake have full time hookups if you want to test that part of your vehicle.
Another area close to Fresno would be around Shaver Lake. Camp Edison is another full hookup spot and the nearby town is kinda quaint. There are several other less populated CG's but not sure which are open. I usually stay in places out of the snowline. The nice thing about that area is there are a few really nice mild all year 4x4 drives to explore if you have the time.
I really enjoy the Kings River just above Pine Flat Lake which is also very close to Fresno. These are boon dock spots along the river as well as a few CG's. The easy Davis 4x4 trail is nearby and doable if it's dry enough.
Another spot I've camped at during winter (my maiden run) is King Canyon NP. Not much open but I stayed at the CG close to the General Grant big tree grove.
Enjoy your trip. I have some info at my web site that talks about some of these areas. Edit if you can find a copy of Backcountry Adventures by Peter Massey and Jeanne Wilson buy it. You should be able to find a used copy.