Near Greenback you have cities like Knoxville, Maryville and Lenoir; but if it is the outdoors you crave, we have several links to hiking, waterfalls and a Sunday drive to the Great Smokey Mountains.
For Hiking we suggest the following websites:

Visit Knoxville

BringFido

Best Dog Friendly Trails in Tennessee

TrailLink

OR maybe it is waterfalls that peak your interest

Chasing Waterfalls

EastTN.US

OR maybe great food is your style

Visit Knoxville

Entertainment, we suggest nearby

Dollywood

Tennessee has a lot to offer, plan your trip with

Tennessee Vacation