This is why we live in the Bay Area...

Nature

Muir Woods: Ancient redwood forest. What could be better?
Mt. Tamalpais State Park: Forest trails and mind-blowing 360-degree view of Marin and San Francisco from the 2.571 ft. East Peak.
Mt. Diablo State Park:At 3,849 ft., the tallest peak in the Bay Area. Hiking, biking, wildlife, camping.
Big Basin Redwoods State Park:More ancient redwoods. In fact, Big Basin is home to the largest continuous stand of ancient Coast Redwoods south of San Francisco. Spans the Santa Cruz mountains to the coast.
Tilden Park: Close to home and packed with fun. Trails, a lake, a carousel, farm animals, and a little steam train.

Museums

SF MOMA
De Young
Oakland Museum

Other Fun Stuff

The Exploratorium & Palace of Fine Arts: More than 600 very cool interactive science exhibits.
Golden Gate Park: It's got it all. You can visit museums, a Japanese Tea Garden, an Arboretum, ride a bike, roller skate, ride a horse, paddle a boat around Stow Lake, etc.
Alcatraz:Island, Fortress, Prison, Park.
Children's Fairyland by Lake Merritt in Oakland.
The Metreon Sony mega-whateverplex.

Of course, there's also wine tasting in Napa, about an hour or so north of us; and Santa Cruz is two hours to the south.