I would not stay at Redwoods National Park region as your base. That is a HAUL from SF and the towns are sleepy at best, run down otherwise. The 101 is a snaky, slow highway up there and the weather can be damp, cold and unpleasant. It is special up there, I love to go and may even retire in that area, but it isn't a good cross-section of CA IMHO. It also is a bit one-dimensional: Rough coast and redwoods. Of course this changes if your main interest is the trees. There is no better place than Norther NorCal for that. But for a good dose of redwood trees and some nice day hikes, the Big Basin will be perfect and on your way to Monterey / Carmel.
Mount Diablo is a good suggestion. Has some nice hikes and a nice drive as well. And close to the city. Or you can bike up it. I do that every now and then.
Keep the questions coming. Maybe you can see what's happening at Laguna Seca during that time as well? It is a great track to visit and watch. Definitely do the 17 mile drive. I am not a big fan of the town of Monterey, but Carmel is worth a half day.
G