What time does your flight get in? Traffic can be nuts so you might want to take BART from the airport since you're near the stop anyway. I think from OAK you have to take a shuttle to the station. Plus if I remember right you pay tolls going into the city from Oakland and that can get backed up.
I would look into buying your Alcatraz tickets now if you haven't already. I'm not aure how far out you can buy them but don't wait until you get there or you probably won't be going. They sell out, especially in the summer.
Pride weekend is in June, not sure when, but depending on where they have events it could affect stuff.
It's a fairly easy city to get around with public transit, which includes the cable cars, and your own feet. If I'm imagining the market street car
@Lain mentioned I think it runs to the Giants stadium but I could be picturing it wrong or using the wrong line.