I would recommend doing a ship's shore excursion here. Belize has some jungle-like areas that might be featured on an excursion, and also has excellent snorkeling and diving. However, these would be longer treks, not close to where you dock, and IMO it's not worth the chance going off on your own. It's an English-speaking country, and very beautiful, according to friends who have been there. Yes, there's poverty, but that's true in much of the world. Why miss out on the chance to see a part of the world you may never get to again?