I live in Paducah and there are several great places to play.
Metropolis, across the river about 5-6 miles away. In Metropolis, the place the play is "Trails Inn". They have about 6-7 bar tables and one 9 foot. It is clean, and no trouble. There will be games and action if wanted.
There are 3 main places to play (several bars too) in Paducah. The best place to play in Paducah is "Side Pockets". The owner is Dickie Todd, and he is player and fanatic about the quality of his tables. He gets his tables covered at least twice a year. There is alot of bank players (probably the game of choice in this room), (including Dickie) and others that I wont name that will (and have) gamble anyone. Buddy Hall plays there almost daily. If you play banks, one pocket, or 9 ball and want to gamble or chose not to gamble, it is IMO the best place. They do smoke in this room, no liquior just beer and soda. Friendly room, and action if wanted.
Maybe another 1 mile down the road is "Jukebox". Pretty big spot, but all bar box. I believe that they went all Diamond tables, but honestly I havent been in there since the change. I have gone there in the past and played in tournaments and $5 game bar box gambling. Probably more available, but thats all I have done there.
Maybe another 1 mile down the is a new place. New isnt true, but accurate. Its "Southside Billiards". The new owner has spent a ton of money and it is nice, clean, mostly new. No smoking but full bar. Several full size tables, several bar tables and one snooker table. The tables are fair but not the quality of Sidepockets. Very pleasant and they may have gambling but it is not known for it.
All have weekly tournaments and these all are places I would send any of my friends or family to play with no worries.
I hope this helps and let me know if you need more.