Whats the best place in the caribbean to stay with beautiful white sand beaches ??

Question

My husband and I are looking to take a week vacation in the Caribbean coming this Feb. or early March (need to escape the cold weather is Illinois!) I went to three travel agents and still cannot make up our minds we have no children yet were a young couple (22 and 25) we want to scuba dive (we are certified) we have gone on two cruises to their we Love St. Thomis andTurks and Caicos but did not like Grand Caymen (seemed to touristy) Plese give us some ideas of where to go with amazing white sand beaches and clear water and if you have stayed there before please let us know of hotels you have enjoyed while there Besides Sandels (to much money for us) the most I am willing to spend with flight and hotel is $4000