Honestly, not really. The train in and out of Cincinnati is limited to travel between Chicago and New York City; however, at those destinations, you can pick up trains to other locations. If, however, you are looking for a leisurely way to travel and see the countryside, then traveling by train is for you. While it is relatively inexpensive to take the train from Cincinnati to Chicago (around $100 RT) it will also take you twice as long as driving. If you don't want to drive yourself and don't want to pay to fly, then you might want to check out traveling via bus. Greyhound fares can be as little as half the cost of taking the train.
