There probably are not many museums about oysters and the history of the oyster industry. Lots of glass cases with oysters and other shellfish, some information on crabs, old photos of the area, a small gift shop, and of course - plenty of duck decoys.
It is free (recommend giving a few bucks though). Most people I spoke to liked this as did we. Nice way to spend a little time in Chincoteague.

This museum was so cool. They had the biggest oysters I have ever seen. When I was there they had a man in the lobby who was carving Decoys. It was pretty cool.

visited here on an Elder Hostel trip. A beatiful day in May. Guides were well informed about history of the museum and their talks were punctuated with anecdotes about local history and legends. The main attraction was a light from the original lighthouse on the island. Very informative and we came away with much appreciation of the life of early lighthouse keepers.