I think you'd be ok in Belize. Touring Caracol was fascinating when I did it several years ago and there are other great Mayan sites in the country too.
Tikal in Guatemala, just over the border from Caracol, is a "don't miss" if the political situation is calm. When I was there guards with military weapons were posted at hotels and other places to protect Americans and other guests from being kidnapped and held for ransom. Seeing rough-looking guys with AKs hiding in the hotel landscaping was a little unsettling at first. As things currently stand I wouldn't go near Mexico.
Thank you. Might not completely strike it off the list, then.
That's okay, Obama's bringing mexico to you.