Here's some fun things to do.
Pacifica, Stinson Beach, and Bolinas Beach are good spots for beginners like me. Ocean Beach in SF is good for more experienced surfers. Santa Cruz is also great.
Pick Up Ultimate
There's a bunch of pick up ultimate games in the Bay (at least 40). I've been to at least 10 different ones and I find it's a great way to meet friendly & interesting people while getting some exercise. Also the sideline banter is top notch.
If you've been to the South Bay, you might have seen the large rectangular structure on Mount Umunhum. I'd recommend driving up there at sunrise to get a nice view of the Bay. On a clear day you can see Berkeley.
Crystal Springs is the reservoir on the West side of 280. It's a great place for running, biking and walking with mile markers along the path. There's also the relaxing Filoli botanical gardens and historical estate. They recently completed a bridge that opens up a longer path.
The Marin Headlands has an exciting steep bike path along the coast. Note that the bike path is one-way until Battery Wallace due to the speeds achieved on the incline. There's also nice hikes and views of the city.
Disc golf is a cheap relaxing sport where you walk through nature and throw discs at things. Every course I've been to is free and discs are ~$10.
Mission Peak is a light hike on the edge of the Bay Area that gives a great view of the Valley. You've probably seen pictures of people standing on the pole at the top.