The Museum of Chincoteague Island is small, local, and useful. It gives context to the pony swim, the island's watermen, decoy carving, storms, shipwrecks, and the practical life of a community built around marsh and sea.
Go early in the visit if you can. Chincoteague makes more sense after you have seen how the ponies, fire company, oysters, clams, and causeways fit together.