The Swanage Museum and Heritage Centre is a small volunteer-run museum on the seafront — entry free, set in a stone-walled former coastguard building — covering the town's history of stone quarrying, smuggling, the coming of the railway, and the Victorian-era arrival of seaside tourism. The collection is small and pleasingly local: maps, photographs, a few quarrymen's tools, a model of the Edwardian pier.
Allow half an hour. The volunteers on duty often know the answers to questions the labels don't bother with, and the small shop has good local-interest books and walking maps. A useful stop on a wet morning, or as a fifteen-minute break in a walk along the seafront.