The drive from NC to Port Canaveral is reasonable, and the Freedom Of The Seas would be a good choice. As Jim said, they are a larger version of the Voyager class ships - essentially stretched so it could accomodate the flowrider and the water park for the kids.
I had a Junior Suite on both of my Liberty Of The Seas cruises earlier this month and they are a great choice. When I return to the Liberty in 3 weeks I have an inside cabin with the clamshell shower. The best way to describe these showers for larger people is: soap up the walls and just start spinning around. You'll have an easier time getting clean.