Agree that it depends on how much you actually want to see the city versus the area. There is not much close to the city. Angel Island might be the closest, but no way would I want to carry all my stuff on a ferry and across the island with an 8 mo old. Check out China Camp. It's pretty close. Samuel Taylor is further, but I like it better. IMO, Lake Chabot is not great camping and in the part of the Bay Area that I think would be the least likely to interest tourists (no offense to anyone who lives there). There are several in the Santa Cruz Mountains, but they are pretty far away to go into SF daily. There is also an East Bay Regional campground in Livermore that you could check out, but it's also pretty far out there.