First off, beaches in Anguilla are amazing! (all of them)

But nothing is walking distance from anywhere, so you need a car for restaurants, grocery store (one decent one in town)

so since you have to have a car, go to numerous beaches! (do not miss Shoal Bay, Meads Bay, and the beach at Cap Jaluca, and Rendezvous Bay)

Day trip to St. Martin for a completely different experience (and to shop, best in Caribbean)

road conditions are fine

I don't know that there's anything within walking distance of your villa but there are a few places that I think are close. And one of the close restaurants is one of my favorites on the island: Barrel Stay in Sandy Ground. Very good food in a casual setting. There are a few casual restaurants in Sandy Ground.

Elvis' Beach Bar is also in Sandy Ground. It's probably the most popular beach bar on the island and Elvis is great. They serve bar food and strong drinks.

We used to enjoy eating at The Dune Preserve with the added bonus of listening to Bankie Banx play. But I haven't been reading good things about it lately so I'm not sure if I can recommend it.

The roads are in pretty good shape. Each time we go to Anguilla there are more and more paved roads. The main roads are paved but do be careful of the speed bumps. They can sneak up on you. The nice thing about driving on Anguilla is that there are so few cars.

There are plenty of high end restaurants on Anguilla. You won't have any trouble finding those.

We've never had a kitchen on Anguilla so no need for us to check out well-stocked supermarkets. We always stay in the West End and rely on Food Ninety-Nine for our drinks and snacks. Here's a list of the grocery stores on Anguilla:

http://www.anguillaguide.com/article/view/125

We often spend a week on St. Martin and then ferry over to Anguilla for another week. I love shopping in Marigot (where the ferry dock is located) so I wouldn't hesitate to head over if you need a shopping fix. There is virtually NO shopping on Anguilla.

You should search the Anguilla forum here on Fodors for trip reports from ejcrowe. She and her husband travel to Anguilla often and she blogs about the trips. Lots of great information can be had by reading her trip reports.

Straw Hat is really delicious. Here is my trip report from 2010 Best vacation ever!
http://www.kristibug.com/2010/10/review-of-our-fabulous-vacation-at-cap-juluca-anguilla/

Dolce Vita is also in Sandy Ground, fantastic Italian food. Ripples and Pumphouse are even more casual. Cove Bay, where Smokey's on the Cove opensfor lunch and dinner and rents chairs is calm waters. If one beach is rough, head to the other side of the island (only 3 miles wide). My favorite beach is Maundy's Bay, the beach at Cap Juluca(public parking near Pimm's)I don't know if theyrent chairs. Great local food at E's Oven, Tasty's, Zara's(near Shoal Bay East), Ken's BBQ and B&D BBQ. Nat's Place (Palm Grove) also rents chairs and has great food (I love their johnny cakes!)

Here's some of our favorites:

Gwen's--great for lunch-beach
http://www.tripadvisor.com/Restaurant_Review-g147238-d2315664-Reviews-Gwen_s_Reggae_Bar_Grill-Anguilla.html

On Shoal Bat East beach there are several restaurants and bars in a row that also rent chairs. One of our favoeires:
http://www.tripadvisor.com/Attraction_Review-g147238-d149418-Reviews-Uncle_Ernie_s-Anguilla.html

Mandeariman is also good but kind of pricy:
http://www.tripadvisor.com/Attraction_Review-g147238-d149418-Reviews-Uncle_Ernie_s-Anguilla.html

Overview of Shaoll Bay East:
http://www.tripadvisor.com/Attraction_Review-g147238-d149418-Reviews-Uncle_Ernie_s-Anguilla.html

We also had fun at Johnno's Bar.
http://www.tripadvisor.com/Attraction_Review-g147238-d149414-Reviews-Johnno_s_Place-Anguilla.html

What's the date of your vacation? We're going end of May! We've only been for one day prior and fell in love! We are staying at Mangrove Villas.

Wondering how you are planning to get there if not via St Maarten and ferry?