The Eastern Band of the Cherokee primarily reside on the Qualla Boundary which is not a reservation, but is a Land Trust. Only unconnected bits of it remain in Cherokee county. The primary parts are in Swain and Jackson counties. Ironically, Jackson county is named for Andrew Jackson.
There are plenty of fun things to do in Swain county, most notably river rafting on the Nantahala. I still have my I survived the Nantahala tee shirt. And at Western Carolina University in Cullowhee near Sylva there is the Mountain Heritage Museum.