We just returned from SF and our family of 8 stayed in 2 apts. there. One was VRBO 201677 (the other has a link from this one). Each apt. had 2 queen beds, so you would need both apts. I don't know if that fits in your budget. One important fact on these is that they are NOT near all of the action. They are, in fact, located by the ocean. You walk out the front door and you can see it down the hill (it is around the corner from the Cliff House). Our family loved staying where we did away from the busy areas, but you do need a car. We were able to get across the GGB easily and get to Muir Woods and Sausalito and we could drive to the Fisherman's Wharf area when we wanted to be real tourist.
The apt. itself is an older building that has been renovated. Each has a nice kitchen with granite or marble countertops. The downstairs is the garage and then there is a second floor apt and a third floor apt. Since we rented both, we had the whole building to ourselves. Marie, the owner, was great about answering questions and getting right back to me.
If this doesn't sound like the place for you, you can search for others on VRBO. I find all of our vacation rentals on there. The problem I found was that we did have cars since we were going to Carmel next and most places didn't have great parking.