Bingley
Veteran
First of all don't say San Fran or Frisco as we'll know you're not a local 🙂.
All kidding aside since you'll be in Truckee go straight to Mono Lake after and trek back towards the Bay to Yosemite via the Tioga Pass (Highway 120). One of the most beautiful drives you'll ever see & experience. From there you can hit Yosemite Valley if you wish. Plenty of campsites along the way. Plenty of SF/Bay folks here to give you additional recs I'm sure.
Good advice. To add some detail to this recommendation, from Truckee you should drive past Northstar over to Lake Tahoe. Turn left and drive around the Nevada side of the Lake, stopping from time to time to admire the views. Continue to South Lake Tahoe, then over to Hwy 88, drive through Markleeville, over Monitor Pass, and drop down to Hwy 395. Stop at Walkerburger in Walker. Continue to Mono Lake, then take the Tioga Pass road into Yosemite IF it's still open (it may not be if there's a fall snowstorm). Detour into the Yosemite Valley -- you may be able to find a campsite on the Valley floor in early October. Take Hwy 120 (a.k.a. the Big Oak Flat Road) back to the Central Valley, and find your way back to SF. Don't go back on Hwy 41 via Merced -- it's too far out of your way.
I strongly recommend losing Redwood NP on this trip. It's not that it isn't beautiful or worth visiting -- it is -- but it's over 6 hours' drive north of SF, and you won't have time to see other sites. Save it for a later trip. If you want to see redwoods, go to Muir Woods or some of the state parks near Pescadero and Half Moon Bay.
For camping near SF, I recommend looking at options in and around Point Reyes Nat'l Seashore. Great for hiking, biking, photography, and lots of interesting places to eat at in Point Reyes Station.
For SF itself, my top recommendations include the Embarcadero and Ferry Building, the Presidio and Crissy Field, and Ocean Beach on the west side of town. SFMOMA (3d and Mission) has a world class photography collection.
Happy to give you more specific recommendations or answer questions in a pm.