The Richmond Rod & Gun Club is 10 miles closer and you don't have to wander through the hills to find it either. They have 200 yards, but you must be a club member. Only used it once and they really weren't set up for prone shooting.
Also w/in driving distance to SF is the Optomist Club in San Leandro. From the Bay Bridge, take 680 south towards San Jose/Fremont. In San Leandro, take the Davis St. offramp and head west. Past to Costco and right before the recycling center (dump), you'll see a chain link fenced in area which is the gun club. It's only 22 miles from SF.
If you want to shoot 200 yards, you can also go to the Livermore-Pleasanton Rod & Gun Club. Cross the bridge and take 580 towards Livermore-Pleasanton. In Livermore, take the N. Livermore exit and turn left (NB). Continue on N. Livermore until you reach May School road on your right. Take May School and it will lead you all the way to the club. Distance is about 50 miles from SF.
There's also a range in Los Altos, but I haven't been there yet. Maybe member Chink can give you directions for that.
Up in Marin there's the Circle S Ranch, but I don't remember how to get there.