Here, Cosby refers to the recreation area at the northeast corner of the park, not the town [1] that lies nearby, outside the bounds of the park. This is one of the least-visited areas in the park, offering hiking, waterfalls, camping, and swimming.
The Cosby Creek provides opportunities for swimming and wading. It is a 2.1-mile hike along the Gabes Mountain Trail to Hen Wallow Falls [2]. Several other hiking trails pass through Cosby, including the Low Gap Trail that climbs 2.5 miles to the Appalachian Trail.
Links:
[1] http://www.moon.com/destinations/tennessee/great-smoky-mountains/gateways-the-smokies/cosby
[2] http://www.moon.com/destinations/tennessee/great-smoky-mountains/recreation/hiking/day-hikes/waterfall-hikes