Anguilla IMHO is an not an island to visit on a budget in what resorts call the Festive Season, when they charge their highest rates. Taxis are very expensive, which is why so many people rent cars. That being said, look into:

Elodia's, at the intersection of Shoal Bay East and Upper Shoal Bay is a great location where you can walk to bars and restaurants enjoying two of the islands most spectacular arcs of dazzling white sand. There is snorkeling from the shore and Junior Fleming can take you to Little Bay or wa

http://elodiasbeachresort.com/rates/

I've seen triple and quadruple rainbows from the area around Elodia'a.

Bonne chance! ;~>

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I would agree that the Caribbean in general is completely overpriced around the Christmas holidays. We avoid this time frame like the plague. If you are traveling on a budget, this is not the right fit.

And please be aware, Anguilla is not well lit at night. That means walking is a hazard, so taxi's would be mandatory.

Why not wait and go after the first week in January? Same place, better prices!!!

Aruba would have hotels, timeshares you could rent from in your price range along with buses.

As others have said, "festive season" is the most expensive time of the year on Anguilla and places that would be in your budget a week before and a week after are not during the holidays.

Reading between the lines I sense that your plan is to NOT be home during that time, so moving the trip may not be an option or may miss the point of the exercise.

I am sure folks can recommend places more off the beaten path that would work for accommodation price wise, but the location would require a car or many expensive taxi trips, even if you hit the supermarket and cooked in a lot, you'd still want to get to the beach and distance would likely be a problem due to the high cost of taxis.

If the point is to be away over the holidays, perhaps Mexico might work and still give you warmth and easy access to food and the beach all in one location?

Look into Le Vue. While not right on the beach, it overlooks Sandy Ground. Beautiful view, and you can walk down a goat path to the beach below, which has great restaurants in all price points. Also centrally located, which can be a plus for taxis.

I’d say it’s doable!

be cautious walking up or down the atv path / goat path from La Vue to Sandy Ground. A yr or so ago the advice from La Vue to guests was to stay off of it due to crime, even if infrequent on the path.

travelerroct: post Irma, more street lights have been added, including very bright bulbs. I would consider it pretty well lit now.

Also check a studio at Fountain Residences on Shoal Bay East, you would be on one of the top ten beaches in the world and within walking distance to beach bars and restaurants:

https://www.fountainanguilla.com/?gclid=EAIaIQobChMIq-6Zhv7a3AIVkKDsCh29BQBTEAAYASAAEgKQB_D_BwE

I was there after the new lights had been installed. My comment still stands. I would not want bright lights everywhere, I would rather look at the stars. That said, the roads can still be very dark at night.