Maybe Dominica? Lots of cool waterfalls. For history, maybe Bermuda. Bermuda is easier to get to, but a bit pricier than the Caribbean as it isn't third world. Bermuda is beautiful, but not much in the way of waterfalls. You need a volcanic island for those.
Try Brazil/Argentina, especially the Iguazu Falls area: http://www.iguazuargentina.com/
Another possibility would be Belize: http://www.travelbelize.org/
Mauritius and the Maldives are absolutely beautiful places to go!
Perfect beaches, clear water, white sand, blazing sun.. What more could you ask for!
Puerto Rico would be the perfect place for you. It has everything you want, and and it is small, so you can get around easily.