The reply telling you to check out TnDeer.com is possible the best advice.
I do not know the Cookville area but when I lived in Knoxville there were a lot of public hinting areas within driving distance (under 100 miles) that are free and some with good deer populations.
The wildlife mgt. areas are good places to start.
Check out the Tenn Wildlife Resource Agency web site, need to spend some time on it. They will give you a name and ph no of a local officer who will be a big help.
Bottom line is it takes some effort on your part to search for them but there is some great hunting places with-in a few miles of Cooksville. I hope this helps.

[email protected] ------West Tn --Carroll County----Westport/Yuma area.