While there are no casinos in Nashville or in Tennessee, there are some that aren't too far away.
100 East Front Street
Metropolis, IL 62960
They just opened a new hotel adjacent to the casino! It's about 2 & a 1/2 hours away from Nashville.
421 NW Riverside Drive
Evansville, IN 47708
They also have a hotel. Casino Aztar is about 2 & 1/2 hours away from Nashville.
For a much bigger selection of casinos (total of 9) - you'll have to take about a 6 hour drive down to Tunica, MS. Call the Tunica Chamber of Commerce for more information if you're interested. You can reach them at: 662-363-2865.