Alcatraz is amazing, I've been several times, and would happily go again. You can get an audio tour which is narrated by former guards and gives you lots of insight into the history of the place. If they are doing night tours, you can also look around the hospital wing, which was macabre and fascinating. I love the place, can you tell?
When you get off the ferry from alcatraz, if you wander down the main road, you'll come to pier 39, which is where the sealions hang out, and a lot of the more touristy stuff is. You'll see the ferry building on that main drag there as well, they have a great market in there on a regular basis.
SF has lots of lovely things to do if you're a tourist, and I can't imagine anyone ever getting bored there so I know you'll have fun. Getting around the city, you can use Bart and the metro if you don't want to drive (I've driven in SF, it's not as bad as london but you do have to watch out for cyclists) Public transport is pretty simple, and not too expensive if I remember rightly. If you're going to be there a few days get clipper cards (like an oyster card) to get on and off all the public transport without having to mess about with cash. Or consider getting uber if you don't have it already.
Monterey is wonderful too, I see lots have people have recommended the whale watching, but I'd add a vote for the aquarium too, it's possibly my favourite place in the world. Carmel by the sea is also stunningly beautiful, and amazing places to eat and drink can be found there.
A lot of people like santa cruz, it's got a proper california beach bum surf town vibe to it, and a lovely beach, it will be quite hot in august though. You can fish from the wharf, and see sealions and other wildlife, plus you have the boardwalk which is kitsch and kind of fun.
Hope you have a fab trip, I spent quite a bit of time over there and would love to go back :)