Chabot Gun Club may be even closer to SF than either Livermore or Martinez. However, those clubs are well-run and have many voice-activated trap houses. Chabot has hand-thrown targets, two houses, and the personnel tends to move at a melting glacier's pace. All are lead-friendly.
Pacific rod and gun is open to the public and is open 11:00 am too 4:00 pm wed,sat and sun. Steel shot only. Valley of the Moon is trap only and open to the public only on wed, and sun. I think. Valley of the moon shoots lead but please check there hours. Both are great clubs.