Kalen has this pretty much correct. Most of our great courses are private; and the great public courses are also very expensive.
So Patrick, it would seem that your Dad is already seeing the best that can be seen on the public end; although the advice to add Pasatiempo remains. No other publics are in this class. But one that might be enjoyable and worth your time is called Cinnabar Hills - it's in San Jose, but has a very rural feel. It's very good fun. Find its website and check it out.
Harding seems to be polarizing; some like it, some don't. I'm in the latter camp. But it too might be worth seeing, if only to play the future President's Cup course. Note it is in San Francisco though and would be a haul from San Jose.
Closer to you will be Cordevalle - if you can access the others, you ought to be able to access this. They do offer some times to the general public, but at a very steep price... I do think it's a very good golf course and the experience is top-notch (caddies, high-level treatment); I just wouldn't want to pay the $200+ they charge for normal public play.
In the end methinks your days will be covered by what your Dad can set up as is. If not, then do try for Cinnabar Hills after Pasatiempo.
TH