If you can head south a bit for an excursion down towards Monterey and the Big Sur area you can be rewarded with some native rainbow trout. Even if you don’t get to fish, you’ll get to check out some beautiful scenery. I’ll second the notion of contacting Leland Fly Shop. They may be able to point you in the direction of some more local costal streams. I’m not sure of the regulations up there (year round as well as seasonal closures for steelhead streams). I think most of the seasonal closures start up in October, so you should be fine. Just make sure you’re not fishing in streams that are running warm, as that will increase the mortality rate of the trout.
If you don’t get to go fishing but have some free time and want to get out of the city, head across the golden gate (awesome drive) and spend some time exploring Muir Woods and Muir Beach in Marin County.