You're definitely not moving to trout Mecca. Right at 2 hrs you can reach the lower Yuba, Putah Creek (the closest) the lower Stanislaus and a couple of other tailwaters on the far side of the San Joaquin Valley. The quality waters of the Sierra are going to be more like 3.5 to 5 hours out for you.
Sorry for that news. The good news is you'll have about the best weather in the world, San Fransisco will be 45 minutes away and the wine country is all around you.
If you fish the salt there are good opportunities for perch and stripers around the bay area, but beware of the ocean, as it'll kick your butt pretty quickly if you're not prepared.
I'd love it if someone could chime in with better trout news. Trust me, I'd be all ears and smiles...-Mike