I'm not sure where you are exactly within Beacon Hill, as it is a fairly large area.

Closest food store is probably the Maho Market, but I only go there for something REALLY quick. For anything more, we usually go across the Causeway and go to Carrefour right by Port de Plaisance or to Super U in Marigot. You have Market Garden on the corner of Billy Folly road, but their prices are out of sight.

Closest casual restaurant--again, depends on where you are in Beacon Hill. You can walk down the beach to Mary's Boon or Karakter during the DAY, about 1/4 mile walk from Beachside Villas. El Zafiro is on the beach below where I GUESS you might be staying, unless you are on Burgeaux Bay. Otherwise, head toward Sunset Beach Bar, where there is also the Sandbox in the Morgan Complex, and then all the offerings at Maho. Several high end restaurants in Maho, including Jax Steakhouse, Moulin Fou, Sublime, etc.

As far as noise levels, we hear music from Karakter sometimes. Otherwise, no.