Block Island is flanked by two lovely lighthouses, one to the North and another to the South. The Northern Lighthouse is in Sandy Point and accessible by road, but is a far way to walk from the main port (cars and bikes are easily available to rent).
There is a museum, which was not opened when we went, but the main building is not open to the public, You can get pretty close though along a beautiful New England stretch of beach. Once summer is in full swing, a hot dog stand is parked in the lot.
The Lighthouse to the South is much more dramatic, set above the stunning Mohegan Bluffs. Several points along the cliffs offer amazing photo opportunities of the red brick structure. The building itself is being restored but the grounds and a museum are open for exploring.