Why yes, there is! And it's well worth visiting!
The Carolinas Aviation Museum is located on the airport grounds, on the other side of the airport from the terminal. It's a ~5 minute taxi ride away.
You can see most of the highlights in an hour's visit, alternately if you're interested in aviation and want to watch the video pieces as well, you can easily spend over 2.5 hours there. Perfect for a layover!
The museum has a good collection of planes, from old to new, and the A320 "miracle on the Hudson" plane too. There's quite a bit of history, information on how flying works, loads of info on the US airways flight, and friendly staff. When you're done, they have a seating area outside where you can watch flights arriving and departing, as it's very close to the active runways.
It takes about 5 minutes in a taxi to get there from the terminal. There's currently (2015) a flat rate $14 fare from the airport to the museum or back again. You can pick up a taxi outside arrivals, and to go back the museum staff will call a taxi for you. On arrival into CLT, head to the Charlotte Information desk in the arrivals baggage area, and ask about the museum. They should be able to give you a discount voucher, and point you in the direct of the taxi queue.