In SF:
The best Japanese food I’ve ever had is at Mifune, in Japantown (Japan Center). While you’re there, I think it’s fun to look around Japan Center, there are lots of shops with Japanese stuff (from food to furniture and decor), plus the plaza has an interesting building/sculpture thing.
They just re-did the Academy of Sciences to be green, apparently it’s something to behold. They had a famous architect design it, the features that most stood out to me were the “hilly” green roof and indoor rainforest. There’s also a planetarium if you like to get your cosmo-geek on, like I do.
The Mission District is an eclectic place with interesting shops and such. I like pirates and have a weird sense of humor, so I found the pirate store to be really fun for a quick browse (be sure to poke around in the drawers and cabinets).
If you like history, you could check out the Presidio (historic buildings in a Eucalyptus forest) and then Fort Point, which you can walk around in and see what life was like for soldiers in the 1700’s. It’s also just underneath the Golden Gate Bridge, which is kind of cool.
Outside of SF:
If you’re going to be going to Berkeley for the concert, I think University Ave. and the area near the university are fun to walk around. There’s a huge outdoor flea market not too far away from there, too.
Sausalito is across the Bay in Marin.. you can drive or take the ferry from Fisherman’s Wharf. It’s a cute little town with little shops and restaurants.
You can also take ferries to Alcatraz (I liked the audio tour) and Angel Island, both historic sites.
There are the Marin Headlands on the other side of the GG Bridge from Sausalito, if you like nature. A lovely drive, if you don’t like hiking. Plenty of trails through different kinds of habitat, lots of birds and wildlife. If you go far enough north, you’ll eventually reach a beach we used to go to all the time when I was a kid. Said beach will be less crowded and more pristine than those on the SF side.
Actually, you may just want to explore Marin, if you haven’t been. There are cute towns with shops and restaurants (Mill Valley and Sausalito), as well as TONS of outdoorsy stuff (Mt. Tamalpais, Marin Headlands/GG National Rec. Area, Muir Beach).