Lots of destinations within an hour's flight of the Bay area.
First up is the "Bay Tour". All you need is a terminal area chart for SFO. Call up ground and as for the "bay tour" and they'll give you a squawk number. Depending on the direction you want to go, they'll give you clearance through class bravo, over the major controlled towers and so on. It's a bit of busy work for the pilot as you'll be talking and changing frequencies. Get a good idea where the major highways and class B areas are before you go. Some of the local airport shops sell a laminated map depicting the bay tour paths, you don't really need one but it is handy. Just keep in touch with ATC and watch your altitudes.
Destinations: Lots. San Carlos has the Hiller air museum, Half Moon bay, Watsonville are favorite local stops for food and scenery. If you want to venture farther, I can recommend Columbia California, the restaurant at Paso Robles is awesome good, Harris Ranch is a great stop for burgers and steaks. Gustine has the cheapest gas in the area that I know of.
On the WX, check your destinations for fog and temps. The bay area has lots of "micro climates." Just because it is hot and sunny on San Jose, there might be fog and temps in the 60's on the coast or up on the SF peninsula.
I've missed some stuff I'm sure, but there are a lot of destinations in the area.
EDIT:
I found a link to the Bay tour map:
http://www.sjflight.com/BayTour.htm
