It's been smoke-free since August.

https://bewell.utk.edu/policy/

https://www.wbir.com/article/news/butts-out-ut-knoxville-goes-smoke-free-wednesday/51-530944220

Cities are creatures of the state and only excercise the powers so granted. Cities' ability to regulate smoking is preempted by the state of Tennessee. While state law does not permit smoking in enclosed public spaces, cites are preempted from instituting regulation beyond that, including in non-enclosed public spaces. See section 4 of 39-17-1804 - Exempted areas.

(4) (A) Non-enclosed areas of public places, including: (i) Open air patios, porches or decks; (ii) Any area enclosed by garage type doors on one (1) or more sides when all those doors are completely open; and(iii) Any area enclosed by tents or awnings with removable sides or vents when all those sides or vents are completely removed or open;

UT, as a state institution, was provided the authority to regulate smoking on its campus.

There was an attempt last year to let cities have autonomy to regulate smoking but it did not pass. The following link provides good context. If such legislation passed then the conversation would shift to Knoxville and would be engaged through the local political process.

"New bill aims to restore local decisions on smoking policies" (link...)

As currently written, the Tennessee Code Annotated 39-17-1803 prohibits smoking “in all enclosed public places” and lists 19 examples. However, TCA 39-17-1804 does allow smoking in “non-enclosed areas of public places” and 10 exempted enclosed areas.

FWIW the issue of what is appropriate state preemption of local authority is a major concern each time the General Assembly convenes.