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.