Another for CBC or Shoreline.
Reposted:
You definitely want to hit the California Billiard Club. It's a well thought out and run pool room. In addition to GCIII's the place has 3 snooker tables (2 of which have traditional snooker cloth and the third is covered to play golf), as well as a heated billiard table. I was up there on business recently myself and spent about 4 evenings there and every time I took a table the balls were freshly cleaned and polished.
The smaller section (towards the street) is the match/tournament area, and is preferred as this is where you will find the tighter tables.
They have monthly memberships (not required) so there is a good group of regulars there. There's action if you want it. The owner's name is Chris I believe and I'm sure he would introduce you around.
Shoreline Billiards is up that way too. Also a good room, Bob Jewett plays out of there. I liked the CBC better though. I think Shoreline caters more to leagues than the CBC.
Both are in Mountain View, about 10-12 miles from the San Jose airport, maybe 10-15 minutes away.