In general Ambergris Caye and San Pedro are safe as long as you use common sense and understand that this island is part a poor developing third world nation.
The island has a mix of locals, expats, and tourists. I am in the process of moving here now and I have not met an unfriendly person from any of the fore mentioned groups.
I have visited many places on the island but still have many areas to explore. I do not know where you plan stay during your visit, but if you limit your evening excursions to restaurants/bars or your hotel/resort areas, you will be fine. I would recommend not going out late at night at least until you become familiar with your area. Leave jewelry and expensive items at home or in your hotel. Do not carry a lot of cash and use you credit card or debit card where you can. Again, use common sense. In general, everyone is friendly but that does not mean that they will become your friend. Enjoy your visit to AC.