Downtown:
https://www.visitknoxville.com/things-to-do/popular-spots/market-square/
https://www.visitknoxville.com/things-to-do/popular-spots/gay-street/
And for a bit more eclectic area, Old City:
https://www.visitknoxville.com/things-to-do/popular-spots/old-city/
https://www.visitknoxville.com/events/
https://www.baxtergardens.org/about/
https://www.visitknoxville.com/listing/sunsphere/567/
https://www.dollywood.com/
https://www.nps.gov/grsm/planyourvisit/index.htm
Recommend Clingman's Dome and Cades Cove for 1-day drives through the national park.
Recommend Charlie's Bunion or Rainbow Falls for 1-day short but moderate hikes in the national park.