Rescue hit on pretty much everything.
Santa Cruz is where it's at, but I understand if its too far out of the way.
Stafford Lake(Novato) is a bit tricky to navigate at points if you've never been there, but if you bring a map (they usually have them at hole 1, you pull in, park and walk down the paved trail until you see stairs and the sign w/ brochures). I am gonna be there next weekend sometime hopefully if weather permits. New players dont like this course because of the length, personally its one of my favorites.
Only played skyline once so I can't say much about it, but I drank a fair amount of beer and had a good time.
Moraga is a fun nine hole course that is somewhat challenging, also the new walnut creek course is close to that one. Played Walnut Creek for the first time yesterday and it's a very small course with lots of intersecting fairways, pretty easy overall (shot even and -1 the two rounds I played)
Do *not* play San Ramon, its a tiny course crammed onto one hillside. Aquatic is my second least favorite course in the area.
If you play Chabot Park make sure to play all of the alternate tees to make it worth your time. This is the closest course to me and if you played by the signs you can use a midrange/putter on almost every shot, so stick to the alternates.
San Jose has Hellyer Park and Parque La Raza within a mile of it, both 9 hole courses and good fun. Hellyer has some nice elevation changes and is typically windy at spots, they did well planning with the somewhat limited terrain. La Raza is more challenging and has some longer holes. I lived in San Jose for awhile and there are a lot of cool players on the SVDGC~
If you have any questions on the bay area courses you can pm me, I tend to bounce around to them all. Have a good time!