What doyou consider extremely far away? What interests do you have? Where are you starting from in Ohio? You could go to Washington, DC to see the museums and historical sites. Toronto is close and a nice place to visit.
If you're driving, there are a couple of good websites for finding interesting things to see along the route:
http://www.roadtripamerica.com/
http://www.roadsideamerica.com/
INdia
Canada
Istanbul, Turkey
Top is NYC.
Lots public transport all over.
It has everything but a beach, altho there is a beach near.
united kingdom