Don't usually reply but this is right in my wheelhouse.
I have stayed nextdoor to White Sands a few times so I do know the local fare. Last 2 week trip in May we ate at (up north)Palapa Bar (my favorite palce for taking fish we caught) , Aji, Akbol (great breakfasts), Capricorn, Capt. Morgans, Cowboy Dougs, the burger palce and the Irish pub. Kept missing the Pirates Villa BBQ but hear it is good (we really miss the Lazy Croc). All were good, Aji and Capricorn are always top of the list.
Take the Island Ferry into town and don't miss Mango's, Blue Water Grill, Fido's, Elvi's, street vendors on the weekends in the square, and breakfast or lunch at Estelle's Dine by the Sea(our all time favorite for over 15 years !)
Loads of others but these are