Downtown Knoxville is compact and walkable. Market Square, Gay Street, World's Fair Park, the Old City, and Volunteer Landing can all be reached on foot within fifteen minutes of each other. The University of Tennessee campus is a twenty-minute walk south from Market Square, or five minutes by bus.
The Knoxville Area Transit (KAT) bus system covers the city, and a free shuttle called the Old City Trolley connects downtown to the Old City neighbourhood. Rideshare services (Uber and Lyft) are widely available and cheap within the downtown area.
For getting to the Smoky Mountains, you will need a car. There is no public transport link to Gatlinburg or Townsend, and the park itself has very limited bus access from those gateway towns. Car hire is available at the airport and in the city.