I think this is probably too much for an arrival day as well. Everybody is different though, so if you are well-travelled and know how your body handles jet lag and are used to arriving in strange cities and hitting the ground running, then it is a decent idea.
If your flight arrives at 10am, plan to be leaving the airport at about 11:30. I believe there is luggage storage at the airport, but I am not sure. The airport web site should give you that information. If you can't leave your luggage at the airport, then you should be able to leave it with a concierge at one of the hotels when you get into SF itself - contact them ahead of time so you know where you need to go.
You can take BART into SF, which will put you downtown (near many full-service hotels). Including time to deal with luggage and get into town, figure it will be 1pm.
For a tour - if you want a guided tour, check out the tours listed on TA and see if any appeal. If you want to just wander around, there are a lot of choices.
Once you are done sightseeing in SF, you can go straight to SJ if you have your luggage - take a taxi to the Caltrain Station at 4th and King and then Caltrain to SJ - Caltrain takes about 60-90 minutes to SJ, depending on whether you get a limited stop train or not. From there, either a taxi or lightrail to your hotel, depending on where you are staying. If your luggage is at SFO, take BART back to SFO and then head to SJ - you can take Caltrain if you want, but I'd probably just take an airport shuttle at this point to save some hassle - I'd be pretty tired by now.