Here are some of the wonderful restaurants in Anguilla.
1.  OLIVERS - Caribbean style delicious fish meals
2. PICANTE - Mexican wonderful fajitas
3. BLANCHARDS - Luxury and the finest quality (lamb rack superb)
4. B & D's - Local on the road barbecue delicious ribs, chicken, fish, chips, salad, and rice.  Ask you hotel about it. Open only on certain days, dine with locals and enjoy great local food. Open Thursdays, Fridays, Saturdays (check at you hotel).  
5. Johnno's - Every Sunday Jazz afternoon good atmosphere and nice food.
6. Tastys- try the pork if it is still on the menu.
7. MALLIOUHANA HOTEL- Micheal Rostang dining, fine food, great view overlooking Meads Bay.  Staff wonderful, food delectable. Apple tart good.  Call ahead and order the rottisserie chicken (30 minutes to cook).

Top fine dining spots: 

Pimms at Cap Juluca- What an awesome place with great service, wonderful food, and amazing view.

Veya - Halfway down the hill towards Sandy Ground, this little restaurant can really deliver. Mondays, Wednesdays and Fridays (in the off-season) try the market menu for $50. You get three courses created by the Chef. The service is friendly and efficient.

Hibernia - a little bit of an adventure to get to since it is on the east side of the island, however, it's worth the trip. Specializing in Asian inspired dishes, including a smoked fish appetizer and the a appetizer.

Jacala - on Meads bay next to Blanchards. Great place to have lunch and look out at the beautiful ocean. good food and decent prices.

Excellent Casual Spots:

Le Bon Pain- Awesome bakery on the east side that is worth the trip. make sure to get there early or call ahead. they sell out of their wonderful pastries very quickly.

 Un Amore Cafe-South HIll.  Excellent Italian earty.  Families welcome.  great pizza and large wine list! 

 Geraud's- in South Hill.  Great sandwiches, homemade bread, wonderful pastries and breakfast.

 E's Oven- also in South Hill has delicious casual dinners, cozy and romantic.

Picante- in the West End.  Best Mexican with a Caribbean twist.  Casual and fun.  Great ribs!