There’s some great riding all over the peninsula. Los Gatos is good and last time I was there there was a good bike shop on Main Street that rented half decent MTBs, HT should do you. Cross the bridge to Marin also, some beautiful places to go and see there with some great coastline. Muir woods is worth a visit. There is some fantastic hiking in the redwood forest just outside Santa Cruz (Fenton IIRC).
Sod the Intel museum and and Apple HQ, if you want to do a proper pilgrimage get yourself over to Marin, rent some bikes, and ride up Mount Tam, over to Repack, etc.
If you just want to do sightseeing stuff, then San Francisco itself is a pretty cool place to just wander around. If you want to do Alcatraz then book in advance. If you’re in Santa Clara, can you move hotels and into SF for the weekend perhaps? Also Napa for vineyard visits etc.