If you have a full day before drinking is commenced, I highly recommend hopping on the Cal-train and swinging up to see San Francsico - it's very affordable and stops along all cities enroute...and you can drink on the train if it's a must.
http://www.caltrain.com/
If you have transportation and have been/have no interest in San Fran, I'd drive down to Monterey and check out the 17 mile drive and the famous golf courses and stunning picturesque landscapes.
As far as San Jose during the day, well, there isn't much to do imo. The only daytime non-drinking activity that I've truly enjoyed was visiting the Winchester House.
http://www.winchestermysteryhouse.com/
As far as weather is concerned, if there's not a pacific storm pushing in you can expect upper 50's/low 60's for highs around San Jose and much, much cooler if you head up to the city.