I live outside of San Francisco, on the peninsula. San Jose would be a long commute to San Francisco. Crossing the bridge would not be a bad idea, but again the commute can be difficult. There are also great hospitals outside of SF, if you wanted to live in San Jose.
I like the Peninsula. It is close enough to the city where you can drive or take public transport. BART can be accessed from Millbrae, which has a great public school system.
Check out
www.craigslist.org under housing to get an idea of the price ranges for rentals and/or buying. Good luck!