Megan, "safe" is a very difficult term to quantify. From my law enforcement background - previous posts have mentioned contacting Palo Alto PD - great advice. I'd actually go there, and talk with the "desk officer" on a personal side, versus calling. Most agencies also provide their crime stats on their websites (google PAPD). The FBI also has each city broken down with crime stats (called Part 1 crimes) I also agree with the HUD post. Do your due diligence - it's really easy.
Palo Alto has been known for their top school district for decades. If you want great schools this is the place for you. As for safety, check Megan's List. Talk to the neighbors on either side of the house you're considering, call the police department. Do the leg work.
Though this is a perfectly legitimate, and common, question, answering this type of question can be risky for a real estate professional because of HUD fair housing laws. I'd encourage you to find online sources of information, such as from the Palo Alto police dept, to help find an answer.