We really enjoyed Bates House Bed and Breakfast a few years back
I have stayed at the Waterfront Plaza a couple of times, but I think they are overpriced.
I haven’t tried the Coral Reef Inn and Suites, but I’m planning on trying it out next time I go over there.
You might also want to look at the refurbished Inn At Jack London Square. I hear it’s nice, but be sure you get one of the renovated rooms, the last I heard some weren’t re-done.

There is always the Claremount in Berkeley. Great views.

@basp The Claremount is a fine old hotel, but with the antique furniture, and (to me) musty smell, it isn’t good for families.