Welcome to Flyertalk!
While I've never been to Anguilla I really enjoyed reading this book and highly recommend it to you in advance of your trip:
A Trip to the Beach : Living on Island Time in the Caribbean
by Melinda and Robert Blanchard
The authors write about their experiences moving to Anguilla from Vermont, living on Anguilla and adjusting to island life and opening up a fine dining restaurant called "Blanchards".
Read the book then eat at the restaurant!
http://www.frommers.com/destinations...la/D39740.html