I'd suggest sticking around the Fresno area for a few days to check for any bugs that might require you to return to the shop. Grab a copy of the California Trails
books that cover the regions you are going through. You might not want to do any off roading but the books are worth having on board.
September can be warm but generally we do see some rain in the Sierra's during a normal season. As the kids head back to school, campgrounds in the parks are a bit easier to score a good site. On the bad side is hunting season begins making it a bit more difficult to find a dispersed camp site.
Places close to SMB:
Kings Canyon area as mentioned has several places to see and the drive down into Kings Canyon will really give your vehicle engine a workout.
N/O the Kings Canyon area is Pine Flat Res off of Trimmer Road not far from Fresno. You can disperse camp along the Kings River plus there are other regular campgrounds along the lake. This is lower altitude camping and can be warm depending on the weather. Toward the end of Trimmer Rd you can cross the river and head up to Black Rock Res past Balch Camp. Black Rock has a very small CG and is in the pines however the drive up might bother some who don't like looking over the edge of steep drop offs
The Davis Flat trail is an easy 4x4 run that connects Trimmer to HWY-180 out of Sequoia NP but requires a bit of off road navigating.
Further North is the Shaver Lake resort area off HWY-168. Huntington Lake and Shaver offer many standard campgrounds as well as full hookup type camping. Several fairly good restaurants are scattered around Shaver. The drive up Kaiser Pass to Edison Lake is beautiful and there are several regular CG's at high altitudes. There are hot springs up there if you're into that.
The Sierra Ranger district above Bass Lake (HWY-41) borders Yosemite and the Muir Wilderness area and is also close to SMB. Beasore Road out of Bass Lake is part of a Scenic Byway that runs through an area full of dispersed camping but also has several forest service campgrounds. Showers are available at Jones Store for a reasonable price and they provide good food.
Down towards Yosemite you can always try the Merced Recreation Area. They’re all primitive camps with vaulted heads but no water and it’s also a lower altitude region so it might get a little warm. The drive into the Park is not too far off. My favorite campgrounds in
Yosemite are Tamarack Flat, Porcupine Flat and Yosemite Creek. Tamarack is my choice because it’s difficult for large RV to get in there and high enough to enjoy a cool night around a campfire. It’s also more central to the park itself making it a good base camp to explore Yosemite. Tioga Pass is well worth driving over to 395. If you have the time you can loop over to HWY-120 (Sonora Pass) via 395. It’s another scenic drive (rivals Tioga) and has a lot of forest service CG’s. If you’re into fishing, the Stanislaus River has some big trout that have been stocked just a few months back. From Sonora it’s only a few hours back down to the Central Valley, I-5 and the Bay area.
I agree that you should consider visiting the Lost Coast area. Glass Beach is a beach in MacKerricher State Park near Fort Bragg is a nice spot to visit and/or stay. Where HWY-1 & 101 meet is Usal Rd/beach. The dirt road can be slick when wet but is an easy drive off HWY-1. Elk will walk right through the campground. The beach is nice. There are several other campgrounds along the coast that are very nice. Prairie Creek and Gold Bluff are good spots. I’ve camped at several places all the way up the coast. One that I thought was great is Jedediah Smith Redwoods State Park. The campground is heavy in cover, has showers, and there is a short one way scenic drive through some Giant Redwoods next by. You can do laundry in Crescent City and stock up supplies if necessary.
You should be able to search the web for info. I have some other information at my web site
I wish you happy traveling from Fresno. Lots to see in CA…enjoy.