We would like to camp near San Francisco next June and be able to take public transportation into the city. Any ideas or recommendations?

Marin Headlands (Kirby Cove) has campsites for $25/night but it has no water.
There are 3 HI Hostels in SF. That's your best option if you want a shower and a real bed.

http://www.nps.gov/muwo/upload/Campi...nty-Master.pdf
Park Service options for the Golden Gate area.

Will you have a car at all? It greatly increases the possibilities.

Consider Angel Island, in the Bay with spectacular views of San Francisco and access by ferry. Reservations accepted 7 months in advance. I have always wanted to do this but so far have only hiked around the island.

http://www.parks.ca.gov/pages/468/fi...andCamping.pdf

The options for camping close to public transit are pretty limited. If you will have a car and can drive to public transit though, that does increase the options.

I think Angel Island is the perfect solution. Ferry to Tiburon and then across to the island. Amazing views and interesting history.

While most rural camp sites have limited) transit connections (or very often, none). Angel Island is sooooo easy.

yes we will have a car but don't want to drive into the city

Angel Island doesn't have parking - but you can park in Tiburon.

The website for CA Parks sited above mentions the possibility of needing to carry camping equipment on Angel Island for "up to 2 miles". I car camp from time to time but am not a backpacker. I think Angel Island would be a wonderful place to camp if that aspect isn't a problem for you. If it is, consider doing your camping any of a number of places north and south of San Francisco and seeing Angel Island on a day trip. If you decide to camp elsewhere there are places to park to connect with public transport for trips into the City.