You may want to rent a car, SF is dog friendly but public transportation does not allow dogs on board. Having said that, I have seen people bring their little dogs on buses in their carrier unknown to the bus driver.
Check out
DogFriendly.comŽ - Pet Travel Guides and City Guides for Dog/Pet Owners or buy The Dog Lovers Companion to California guide... just be sure to get the latest edition. I would also advise to double check and call restaurants and places you wish to visit ahead of time ask if dogs are allowed in case they've changed their policy.