The best time to visit is May through October. Summer (June–August) is peak crab and fishing season — blue crabs are in full abundance, the Chesapeake is warm enough for boating, and the skipjack sailing trips are operating. It can be hot and humid, as is Maryland's summer, but the water keeps things tolerable.
May, September, and October are the best months for birding — the Eastern Shore is on the Atlantic flyway, and migrating shorebirds concentrate at Black Walnut Point and around the bay. Fall is also the prime time for the rockfish (striped bass) run that draws charter fishing boats.
The skipjack oyster dredging season runs from October through March, when you might actually see the boats working under sail. Winter is quiet but the island doesn't close — watermen are working all year.