I think most people, including single female travelers, feel pretty safe in most areas of the mainland. Belize City, Dangriga and Orangewalk Town can be a bit rough, but even there with caution you will be okay.
Many of the jungle lodges in Cayo and elsewhere are set up in a way that makes them comfortable for single travelers. Several of them don't even have locks on the doors, as they are entirely safe.
There are of course many ruins in Belize, at least a dozen major sites and literally hundreds of minor ones. They are all different. Quite a few of the lodges, including Chan Chich and Ek'Tun are literally built on an ancient Maya site.