I would highly recommend Drakes in San Leandro. Only about a 20 minutes drive from where you'll be. Really good west coast ales and a cool tap room.
http://drinkdrakes.com/If you're going to Anchor you might want to check out 21A (tasty crack cans....tasty crack cans...) or Speakeasy. 21A has a nice big bar and usually has some unique collaborations on tap but it can get super crowded, luckily baseball season is over so it's probly not that bad. I've never been to the taproom at Speakeasy but I love their Big Daddy IPA.
Sierra Nevada opened up the Torpedo Room recently in Berkeley. I posted this on another thread, never been there yet but hear good things. Triple Rock is also in Berkeley, word on the street is you might find Tasty McD there.
If you're a fan of sours, even if you're not... I would HIGHLY recommend going to the Rare Barrel. All sours on tap (I think there's 6 or 7 different ones). Pretty sure they are only open Friday and Saturday but definitely try to check this place out.
This should give you a head start, cheers!