North Carolina
Ashe County quiet, on one of the oldest rivers in the world.
Fleetwood sits in Ashe County along the New River, which despite the name is one of the oldest rivers on earth and is protected as a National Wild and Scenic River. The water is shallow and gentle, which makes it a floating and tubing river rather than a whitewater one.
Boone is about half an hour south when you want more going on.
Nearby

Seven accesses along a National Wild and Scenic River, with free day use and gentle paddling.
Official site
Shallow and slow enough to float or tube, and good for fishing and wildlife watching.
Official site
Ashe County's small downtown, with galleries, murals and a cheese factory.
Official site

The northern stretch runs close by, with some of its quietest overlooks.
Official site
A 1914 country store on the New River, alongside one of the state's most scenic bike rides.
Official site