Um Jack, does a bear poop in the woods??? 

Well, if you want to drive out to Norfolk/Newport News you've got: 

Nauticus: really nice aquarium and the battleship USS Wisconsin.

The Mariner's Museum: so much stuff you can't see it all in one day! Plus an entire roomful of incredible scratch-build model ships. And a full scale mock-up of the USS Monitor you can walk around on. 

A little off the side The MacArthur Memorial is pretty cool too.  

There are a couple of other cool military museums in the area too, mostly army stuff though. 

The Yorktown battlefield is a pretty neat place to visit and close to Williamsburg too.  

Don't miss the three replica ships at Jamestown - less than an hour from Williamsburg.  They are reproductions (based on a great deal of research and informed guesswork) of the three ships that brought the first English colonists to Virginia in 1607.  Highly recommended.

I'll second Prof. Tilley's recommendation to see the three ships at Jamestown. I've lived in this area of Virginia for 32 years and finally visited them last year. Wow!

The USS Wisconsin at Nauticus and the USS Monitor's artifacts at the Mariner's Museum should not be missed, neither.

There used to be tours of the Norfolk Naval Station but I don't know if they do that anymore. There are tour boats that do the Naval Station Tour, though, and I think that is a better way to see it, anyway. Just do a drive on the I-64 Loop and you can see the Naval Base, Naval Shipyard and Newport News shipyard where the USS Gerald Ford is being built. The island structure has been installed on the flightdeck. The Enterprise is in port as are other carriers. It is a good time to see the fleet as the sequester is keeping a lot of the ships tied up to their piers.

Also, there is a lightship museum ship in Portsmouth. Williamsburg is about twenty minutes from Newport News and about 40 minutes from Norfolk.