I wouldn't just think about music in San Jose. It's really about the Bay Area. San Jose is somewhat the southern tip of it all. San Francisco is a trivial drive to the North. Plus you have the East Bay corridor heading up into Oakland, Berkeley, and Concord.
A couple of hours Northeast of the Bay Area: Sacramento.
Santa Cruz is 30 minutes south of San Jose; Monterey, about 30 minutes further down the coast. Monterey has two music festivals of global reputation: the Monterey Bay Blues Festival and the Monterey Jazz Festival.
Within a couple hours of the Bay Area, you have access to all kinds of music and scenes.
Jaco died for our sins so that modern bass players could be free to play more and be heard.