You could spend the whole time in the SF city limits and have a great time. I'd be careful about how much driving you do. If you're not familiar with the local traffic patterns you might waste a lot of time on the freeways. There are better things to do here than drive...
Personally I'm not a big fan of wine country tours, and be aware that it can be really hot in Napa in the summer with bad traffic. I do, however, think the Alcatraz tour is worth doing. I did it a year or two ago and found it to be very well done, plus you get a ferry boat ride on the bay, hikes on the island and it's an incredible vista point. If you don't do Alcatraz at least walk or bike on the Golden Gate. I'd also suggest going out to the Haight-Ashbury district and poking around... at least if that means anything to you... or check out SFMOMA...
I think Monterey is a bit far... consider places like Muir woods and Stinson beach up in Marin County, or go a bit down the coast to Half Moon Bay or even Santa Cruz. You can even go to the beach right in SF... Ocean beach is a long beach and Baker beach is right by the Golden Gate... clothing optional at one end
