Cincinnati has one of the best Zoos in the country, they also have one of the best fine arts programs in the country and the museums are very good. The symphony is one of the best as well as a lot of local places that are family friendly for music.
Coney Island has a small section with rides and one of the largest fresh water pools in the country.
Grade school kids would love Kings Island and the Airforce Museum in Dayton is a great attraction but close to 2 hours from Big Bone Lick.
Newport Aquarium as mentioned before is pretty cool and there are plenty of places to eat there. The Natural History Museum is great in an old dome shaped train station, there's an I-max theater there that usually has good movies and they have many children's programs.
You have to let me know what you think of the Creation Museum and Ark, I live in KY and many are not too happy that tax payer dollars were spent on it. It's a pretty sore spot with many residents in the area and I'm curious to hear what someone not from this area thinks about it.
Lots to do around here, If you do decide to head towards Lexington and the KY Horse Park, about an hour further south east from there is Red River Gorge, Natural Bridge and Daniel Boone National Forest, absolutely gorgeous area and plenty of camping available.