Round Grove, IN. You might as well go on to Lafayette.
Halfway between Columbus and Cincinnati
Cincinnati is he halfway point between Dayton Ohio and Lexington Kentucky. There are 135.61 miles between the two.
Benezette, Pennsylvania is the halfway point between Long Island, New York and Toledo, Ohio. There is approximately 604 miles between New York and Ohio.
Ohio is almost 45000 square miles and the halfway point from Cleveland would be different from the halfway point from Cincinnati. Columbus is centrally located. That halfway point is Miami... West Virginia.
Dayton Ohio
Beckley WV or Covington VA are close to halfway and have hotels and food
If Driving, the halfway point would be in-between Nashville, TN and Memphis, TN. There is no good town indicator. Mile 143 on I-40 might be a good halfway point.
One halfway point between the city of Little Rock, AR and Lewistown, PA would be Cincinnati, Ohio. Cincinnati, Ohio is close to Northern Kentucky which has many things to do.
Evansville Indiana
Sugar Grove, Ohio is the halfway point.
Silver Springs, OH is the halfway point.
A halfway point between Crossville, TN and Fayetteville, NC (depending on your route) is Vein Mountain, NC.