The first thing that comes to mind is the movie Night at the Museum with Ben Stiller.  My boys were obsessed with that movie when they were older and always talked about wanting to stay overnight.

Who knew there are tons of places within driving distance of the tristate that will allow you to have an overnight experience.

Newport Aquarium in Northern Kentucky gives you an entire experience;

Behind the Scenes tour
Guided aquarium tour
Animal encounters
Themed activities
Evening snack and light breakfast

The price is super cheap too and you even get in free the next morning after you spend the night.

Louisville Zoo Overnight Safaris sound like they would be a blast.  While you're there you get a presentation on the animals, guided tour and educational activities.  You have a choice to sleep inside or outside near the Snow Leopard Outlook Pass.  When you wake up they even serve you breakfast.

Nashville Night Owls Overnights include;

Experience Nashville Zoo after dark for a WILD adventure. Night Owl Programs are designed for groups of all types, ages 5+. For Girl Scouts, Cub Scouts and American Heritage Girls we offer programs to meet badge and adventure requirements.

Night Owl programs include; ed-zoocational activities, games, and crafts. Experience the Zoo with a guided walk at night and in the morning. Plus, meet two of our Ambassador Animals! A light evening snack and morning breakfast are provided along with admission to the Zoo following your program.