The US Army bulit the MH-1A. It is a pressurized water reactor and the first floating nuclear power station.
It was retired from service in 1976 since the Army Reactor Program had been discontinued, and, as a unique prototype, operation cost for the unit was high. It was orginal bulit to supply power to the Pannal Cannal.
The power plant was removed in 1977 and the ship itself was placed in reserve in the James River Reserve Fleet. Not sure what happen the ship, but the power plant was placed in safe storage which means it could be dismatled until 2037. 60 years after it's defueling and shut down.
Here's some more info
http://en.wikipedia.org/wiki/Army_Nuclear_Power_Program
http://en.wikipedia.org/wiki/MH-1A
I think this could another option if you did not want to go with the carrier. You could have anchored at Fort Belvoir (The site storage site of it's old reactor)under refit for active service when bombs drop the base is far enough from Washington and maybe Camp David? The US Army also SM-1 reactor their which is also in Safe Storage.
I think the setting alone is good.