Cromwell's Barracks is the island's strongest historical sight, a ruined fort on Port Island at the mouth of Inishbofin Harbour. It was built in the Cromwellian period, when the island was used as a military outpost and prison.
The setting is half the reason to go. The walls sit low over the water, with the harbour behind and Atlantic weather moving in from the west. Check tide and access locally before walking out.