The Hampton Roads Naval Museum occupies the second floor of Nauticus, the maritime science centre on the downtown waterfront. It is entirely free and well worth the time. The exhibits cover 225 years of naval history in the region, with particular strength on the Civil War ironclad battle, the two World Wars, and the Cold War submarine era.
Moored just outside is the USS Wisconsin, one of the last Iowa-class battleships and at 270 metres one of the largest warships ever built by the United States. You can tour the main deck and several interior spaces for free. The combination of the museum and the battleship is a half-day in itself.