How different is staying in Palo Alto vs SF? And how long does it take getting between the two?
Caltrain will probably get you between the two in somewhere between 45 minutes and an hour on a weekdays. Weekends, you're screwed. Trains run once an hour at the best of times, and are basically broken all weekend due to maintenance for the foreseeable future. (I think they're using buses to connect gaps in service on the weekends).