If you're driving, leave your luggage in the locked trunk in a secure garage in SF. No way I'd drive all the way back to SJ just to pick up luggage left at a hotel.
If you want public transit, take Caltrain from SJ to the Millbrae station, the the BART connection to SFO.
https://www.flysfo.com/faqs
Baggage storage is exclusively available at the Airport Travel Agency, located on the Departures/Ticketing Level of the International Terminal, near the entrance to Gates G91-G102. The Airport Travel Agency is open daily from 6:00 a.m. to 11:00 p.m. No reservations are required for baggage storage. All baggage is x-rayed prior to storage. Rates are assessed per each 24 hour period that an article is in storage (articles in storage for less than 24 hours will be subject to the 24 hour rate), and vary according to the size of the object. Please contact the Airport Travel Agency at 650.877.0422 or
[email protected] for additional information.
Then take BART from SFO into the city. All sorts of great things to do there.
If you have a car, you could also drive over to the coast, maybe Santa Cruz, a fun beach city, the drive up the PCH to highway 92 and head back over the hills in the evening.
It all depends whether you have a car and what you want to do.
Have fun!