I just got back from Belize last Friday, went to Caye Caulker with my best friend for her 50th birthday. Caye Caulker is a 45 minute water taxi ride across the Gulf of Mexico, cheap as hell to eat & drink there. The Belize dollar is equivalent to $2 U.S., the local beer of choice is Beliken or Light House which you can buy for about 2 bucks american. This island is really off the grid, I'll compare it to Gilligan's Island. No cars, only golf carts and bikes. There is one main street with a few bodega's, fry jack huts and bars and a shat ton of street bbq. While it wouldn't have the hiking you're looking for the experience is something that a 14 year old will never forget. The island is so small you can see an ocean sunrise and sunset. Small beach on the tip of the island with a full service restaurant/bar.
Airfare from Syracuse was $725, Delta has 2 flights a day from Atlanta to Belize City on an Airbus with plenty of free entertainment. Here is a pic of main st. You could stay on the mainland and go see the Mayan Ruins and take a few days to stay on Caye Caulker or San Pedro