I can think of three published magazines/books which are stocked at the airport, dock and businesses around the island. I don't know if they send out material, contact them and see.

What we do in Anguilla:
https://whatwedoinanguilla.com/magazine/

True Anguilla:
https://trueanguilla.com/magazine/

Skyviews (a dining guide and map)
http://www.skyviews.com/anguilla-map/

Good luck,
Ellen

If you are on Facebook, join the 33 Beaches FB page, it is a closed group made up of dedicated Anguilla addicts.
Happy planning,

Life's a beach