Chicago to NY rounds to about 800 miles, and takes about 14 or so hours to drive with minimal stops. Cleveland is about 7 hours away from Chicago (about 350 miles away), and I-80, the main route to NYC from Chicago, passes just south of the city, so it is basically half way. Pittsburgh is about 500 miles away, so if you're not looking for the exact half way that works too. But other potentially interesting cities about 7 to 9 hours to the east like Pittsburgh, Cincinatti, etc are all out of the way if you're going to NYC.
Cleveland has the Rock & Roll hall of fame, and NASA's Glenn Research Center among other things. The best of the other cities I listed out of the way is Pittsburgh, which has the Andy Warhol museum, and some really beautiful views of the start of the Ohio river and downtown from bluffs across from downtown (with inclined railway going up and down the bluff).
Columbus, IN is halfway between Chicago, IL and Nashville, TN. There are 441 miles between Chicago and Nashville, and the driving distance is 7 hours and 24 minutes.
Springfield, Ohio is almost exactly the halfway point.
around Hannibal, MO
Chattanooga, TN
The halfway point between Nashville, Tennessee and Philadelphia, Pennsylvania is Harmon Forest, Virginia.
Nashville, TN is a good option. It's only 10 miles from the exact halfway point (Solitude Acres, TN) and is off I-65.
Egypt
Nashville, TN
Nashville, Tennessee is halfway between Buffalo & Houston
going on I65
Willisburg, Kentucky
Maps.google.com
Nashville, TN
Cave City, KY
amsterdam
Cox, Ohio is halfway between Detroit and Jonesborough