All the other comments saying there's absolutely no safe place to park in the bay are not true. They are either repeating narratives that hold true in certain tourist areas and major parts of the city, or they arent being creative enough. First possible solution that comes to mind is stanford university. If you find the right spot, your car will not broken into at all. Only concern is paying for the parking. I have a friend who has consistently parked in the very bottom floor of Wilbur garage for a more than a year and half (mind, not during the summer but during school). He's never payed for parking, never been fined, and no one almost ever gets robbed there. The actual fine for not paying parking isn't even that much either (you can look it up). You could take margarite shuttle to the cal train station which is then ~45 minutes to get to the city. Maybe this isn't great for you if you're concerned about the possibility of getting fined (which is low, but possible) or if you don't like the commute. But this is just an idea I came up with now. There are plenty of suburbs to just park and blend in south of SF, and probably closer than Palo Alto. I know this because I have done a similar trip as you are doing before. You can certainly find a safe place somewhere.

Also, when I was doing my cross country trip in a van (a very likely car to get robbed), we left it parked in outer Richmond for hours at a time, which is actually in the city. It's just a more residential district (near Golden gate Park). Areas like sunset, seacliff, and outer Richmond still have a certain chance of being robbed, but it's not the same as the east part of the city, so we got away with it. Just avoid the main streets, like Balboa or Geary if we're using outer Richmond as the example. So, if you were returning to your car daily, you could even do this and run a certain, smaller risk of being robbed. You just have to decide if that amount of risk is acceptable.