Top counties for P&Y Entries are: Montgomery, Shelby, Robertson, Anderson, Roane
Top counties for P&Y Entries per Human Population are: Stewart, Pickett, Van Buren, Humphrey, Jackson
Top counties for P&Y Entries per Square Mile are: Montgomery, Anderson, Roane, Robertson, Shelby
Montgomery County comes in at #19 out of 95 counties when it comes to P&Y per population, which isn't shabby.
5 minutes of googling reveals Fort Campbell and Haynes Bottom WMA. Fort Campbell is pretty big and I actually know some guys who hunt the Kentucky side of it and do well. Haynes Bottom has boat access and is 1000 acres and bow-only.
Cumberland River runs through the county, but I can't see if there is COE or utility property open to hunting without digging deeper than I care to right now.