Was there for two weeks over Christmas. Unless they've done maintenance on the River Road it's pretty much only passable via high-clearance vehicles and I'd recommend 4WD. Always used to be the East end up to the old mine was passable with any car, but not this year. I did drive the whole road in a Jeep again this year.
Rio Grande Village is the only place in the park with hookups and the cost is about the same as the campgrounds up in Study Butte and Terlingua. There are a lot of dry camping spots in the NP campground right next to Rio Grande Village though. Most than half allow you to use your generator between 8am-8pm. There's a dump and water facility near the Village Store.
The best place, and least expensive, for full hookups is the Barton Warnok Visitor Center which is the Big Bend Ranch State Park HQ in Terlinqua. They have 5 full hookup sites for park volunteers and if they're not occupied they'll let you stay there, but it's first come first served.
Maverick Ranch is one of the best commercial campgrounds with full hookups and all the other amenities. They were full up right after Christmas though. Not sure how it might be now, but I suspect the snow birds have moved in and won't leave until around March.