Unfortunately, one of the best museums along the East Coast - the Refuge Waterfowl Museum has closed forever and the contents and building sold off to some "Beach shop".
Definitely hit up the Ward Brothers Museum. We'll worth the price of admission.
The Have De Grace Museum is pretty awesome too. Look it up for the trip home. It's located at the northern end of the Chesapeake Bay, but the name of the town escapes me at the moment.
There are plenty of things to see along the DelMarVa Peninsula. On Chincoteague itself there are a few little shops and museums. Chincoteague Museum is nice. Make sure to look up Rowe "Duckman" Terry. He has a really neat little shop on the North end of the Island. Decoys, Decoys, Decoys is a little shop to visit, but I would never buy any of the overpriced decoys. Some of our favorite restaurants are located there too. The Village, om Maddox, AJ'S on the Creek, and of course - bill's on Main Street are all great.
You'll most defiantly take a drive over to Assateague while you're there. Make sure to drive the Wildlife Loop after 3 pm. Take binoculars or a spotting scope too. Too many opportunities to miss. The Refuge Visitor Center is worth a stop, as is Tom's Cove Visitor Center. There are quite a few opportunities to take a walk on the island, but make sure you have lots of good bug spray. That area is known for having LOTS and LOTS of extremely undernourished mosquitos. Millions of them!
And then, of course, is the Beach! If you go later in September, or in October, November, the fishing can be very good along the sand, or in the bays. Crabbing! Delicious little buggers as well as Oysters and Clams abound too.
That should give you a pretty good start. Feel free to pm me for more details if you'd like.
Jon