Anguilla is an outstanding island with wonderful beaches and a few excellent hotels. If you are looking to go luxury then I'd recommend the Malliouhana Hotel.
http://www.malliouhana.com/ The Malliouhana has amazing food and probably the best beaches of any of the hotels on the island. The food blows away the CuisinArt Resort and Cap Julca which sometimes get rated better, but really are not better at all. In fact the food is probalby the best in the entire Caribbean at the Malliouhana. The CuisinArt has a great beach as well and some really nice rooms and a very nice pool as well.
If you're not trying to see how much you can spend on rooms and food there are a few other hotels on Anguilla which are also nice with good beaches.
If you want more to do than spend time on the beach and eat, I'd highly recommend Barbados. Barbados has great shopping, a little bit of nightlife, good restaurants, a wide variety of hotels and some pretty decent beaches.
Have fun!
Jedi