I'm a San Jose native, and I can help you out with this one.
Depending one where you'll be, Los Altos Rod and Gun Club Range may not be too much of a drive. (From my parents' house it's about 20 minutes, it isn't really in Los Altos.) It's an outdoor range with 7, 25, 50, and 100 yard lanes as well as a shotgun area. Fairly big, not too crowded, lots of light. $15 if I remember correctly.
Here's the address: 14750 Skyline Blvd, Los Gatos, CA
and phone number: (408) 867-3106
There's also San Jose Municipal Rifle Range at
1580 S 10th St, San Jose, CA
(408) 275-1738
I've never been there, it may be members only. Give them a call though.
Another one: San Leandro Rifle & Pistol Range
This may be more of a drive for you (probably about 45 minutes to an hour).
It's at 3001 Davis St, San Leandro, CA
510) 638-9605
Apparently this range is part indoor, part outdoor, although I haven't actually been there myself.
Having said all of this, I highly recommend Los Altos Rod and Gun. I did most of my shooting up at my buddy's house on private land, but when I did go to the range this was it. The drive isn't terrible, and you get to see some awesome scenery. The staff is great too; had a guy help me out with a friend's broken/jammomatic .22 once, and they even gave us a free pass to come back since we couldn't get the rifle to work (we did get it clear, however). The RO's really jump on unsafe behavior too. I felt very comfortable at all times.