Did that area in 2010, Yosemite was very busy still especially in the valley itself. Outside the valley the campgrounds weren't totally full. We only had reservations for the campground in the valley , rest of the time we winged it but in a camper van so fairly small rig so we fit in almost anywhere.
If you can day trip, take a drive over Tioga Pass and see Mono Lake, stop at the
Mobil Gas Station for a bite to eat, awesome food.
Kings Canyon was having a forest fire on our trip so missed it but stayed in some nice forestry sites in Sequoia, one called
Stoney Creek