Honestly, the Peninsula/South Bay is a pretty boring place to spend a full month. Most downtown areas that people are recommending are charming for a day, but they're all very similar and are primarily shopping/eating oriented. I spent 6 weeks having to hang around San Jose for ~4 hour stretches a few times a week while my sister was still in school and there are only so many times you want to walk around a mall (and I love shopping). I ended up spending most of that time reading in a Target parking lot. And that's not even a fraction of the time your girlfriend will have to kill.

If she is really into outdoor sports and she has access to car, I could see the trip being worth it if she did a ton of surfing hiking/surfing down near Santa Cruz. Otherwise, I cannot imagine this trip is actually worth it for her.

SF is really the only place that has enough "site seeing" to fill a month's worth of time. But realistically having to spend 1-1.5 hours each way to either BART, Caltrain or drive to the city from San Jose is going to suck. She absolutely will not want to spend up to 3 hours every single day hauling herself up to the SF and back. (Not to mention BART and Caltrain only hit limited spots in SF and she'd likely have to spend quite a bit of money or time on Ubers or buses to see most of the city anyway).

These suggestions, while helpful, are not being super practical. Unless she is actively looking forward to just reading outside in a park, this might not be an ideal trip for her.