Most people are trying to move in the opposite direction. With that being said, here's a few interesting things about Ohio:
1. Vehicle safety inspections are not required
2. It's very flat, but their flag is the only non-rectangular state flag
3. Due to an oversight (congress never voted -- oops!), Ohio was not officially admitted to the union until 1953.
If you want stuff to do within a reasonable distance you might want to look at the eastern side, near Pittsburgh.