From the USCF site (uschess.org):
SANTA CLARA CA. SANTA CLARA PARKS & REC CC (USCF ID A6032794). Affiliate Type: Club. COMM REC CENTER, SANTA CLARA. Contact: ALEXANDER VEKSLER. Contact Phone: 650-996-5924.
You can also find plenty of chess tournaments in California through the website. From the main site, just click on "Clubs and Tourneys," then Upcoming Tourneys and search by state. There's plenty in California, I just don't know which ones will be close to you.
Does anyone know if there are any OTB tournaments in Santa Clara, California? Or even clubs for that matter?