Oh excellent that you have a car! that means you can run till you drop on the various trails in the Marin Headlands just over the Golden Gate Bridge or just a bit further north to Tennessee Valley for some coastal (hilly) runs or wee bit north still to Mt Tamalpais where the trail system is endless. So much so that in my decades of being here, I've yet to know all of them. Do a search on the Dipsea Run to get the route for an iconic race in Marin, it has some unfathomable number of steps and elevation gains/drops that take you through redwoods (Muir woods) to the Pacific. Stunning. That's also in the Mt Tam/ Muir Woods area.
Drive to the East Bay and you'll be spoiled for choice in the series of parks that span the east bay hills from El Sobrante ( one end of the Wildcat Canyon trail in Tilden Park) down to Lake Chabot Park and all the parks in between. Tilden Park has all kinds of wooded to open exposed trails that take you through cow pastures, lakes and stunning views back across the bay to SF.
My local secret park is Briones. Past Tilden heading East. Very peaceful, great hills/views and you feel as if you are in another country.
Check before you head out as there are about 100 parks in northern California slated for closure because of the budget crisis and I don't know what parks in the area ar on the kist and when they will close. about 6 years ago
Sorry, one more thing. If youre looking to be social do a search for a Hash Run that may be going on when you're in town. Great group of people who know how to have a good time ( their tagline is 'drinkers with a running problem'). There's usually one somewhere every weekend (all over the world too!) about 6 years ago