The Seaplane Harbour is one of the finest museum experiences in the Baltic states. The building alone is worth the visit: three massive reinforced concrete domes from 1916 that required nothing but their own geometry — no internal columns or supports — to stay standing. Today they shelter the Estonian Maritime Museum's collection, which includes historic ships, a 1930s submarine (the Lembit, one of the oldest preserved in the world), seaplanes, and an excellent exhibition on Estonian maritime history.
The museum is on the Kalamaja shore, about 2 kilometres from the Old Town. Kids and adults both respond well to the scale of it — you can walk through the Lembit submarine and stand under the enormous dome beside a restored seaplane. One of the best museums in Tallinn, full stop.