There are lots! So here is a link to the places in San Jose. And a link to the places in San Francisco.
Largest Chinatown outside of Asia - Food and shopping!. Here's a map.
For the kids
Aquarium of the Bay is right in San Francisco. Here is the info.
Monterey Aquarium - a 1.5h drive way, but a great aquarium!
886 Cannery Row
Monterey, CA 93940-1085
(831) 648-4888
San Jose Museum of Art (FREE!)
Rosicrucian Egyptian Museum (loads of artifacts)
Winchester Mystery House (not spooky at all)
The Tech Museum of Innovation (good for kids)
The Children's Discovery Museum (good for kids)
San Jose Historical Museum (great for history buffs)
Fisherman’s Wharf in San Francisco - vicinity of Embarcadero & Taylor St. Restaurants and shopping.
Santana Row (expensive designers)
Valley Fair Mall (expansive)
Great Mall of the Bay Area (Outlets)
Farmers Markets Around Town
Willow Glen (Saturdays 8:30-12:30)
Los Gatos
Campbell (Sundays 9-1)
San Pedro Square (Fri. until 2)
Muir Woods National Monument. Check out the giant redwood trees, 11 miles north of the Golden Gate bridge. More info.
Municipal Rose Garden (pretty in Spring)
Happy Hollow Zoo and Park (small zoo, good for young kids)
Japanese Garden (large koi pond, pretty scenery)
Lick Observatory (great view)
Hidden Villa in Los Altos (hostel & organic farm)