I'll second the suggestion of Belize. I went there for almost two weeks for my first real vacation, and it was awesome. You can do the whole backpacking thing if you want (which is what I did), or you can just pick a spot and chill. Specifically, I would recommend Caye Caulker (beautiful little island about 1 1/2 hours from Belize City by water taxi) or San Ignacio (near the Guatemala border, and there is this awesome little place called the Parrot's Nest just outside of town).