Hotels in Alcoa near the airport are convenient and mostly newer or updated. Published cab fares from the airport are $25 each way. Nearby hotel rates are probably similar.
As an example, La Quinta room rates for Thursday's game are $142 Wednesday, $149 Thursday, $129 Friday and $105 Saturday, two day minimum. They do not have a free shuttle, but use Rocky Top Shuttle Service, est. $20 each way.
Others are probably similar.
It is about 13-14 miles to Neyland Stadium, usually about 20 minutes but a little longer on game days. Four lane highway straight into town with no traffic lights or congestion until you get to Neyland Dr. There is construction this year, but all lanes are usually open and traffic is flowing with minimal delays.
P.S. Avoid "budget" hotels on Alcoa Hwy.