US Grant birthplace is roughly an hour away- depending on what side of town you're in.
The monument to George H Thomas is in Fort Thomas- a neat community with early 20th century post buildings still occupied. There is a Fort Thomas museum.
You are close to the route of Morgan's Raid. Not sure if a driving tour is posted- but doubt much to see anyway.
Cincinnati Museum is in the old Union Terminal. US Air Force Musem is up the road near Dayton. Newport Ky. has a nice aquarium.
If the Reds are in town, take in a game. And Cincinnati has always boasted a top-tier zoo.