From an old thread, Jackie gave us these two links:

http://www.dogfriendly.com
and
http://www.petswelcome.com -

the first lists a place in Knoxville:

http://www.dogfriendly.com/server/tr...sstateTN.shtml as well as many more - by city, didn't know where you were interested in ...

And dogfriendly lists 8 hotels in TN, first try!