OH is home to 3 large amusement parks, but unfortunately Columbus is more or less 2 hours away from any of them. I haven't been to Kings Island in a very long time so I can't comment on that one. Cedar Point is fantastic if you are a Roller Coaster fan. With 16 coasters (2 of which are for kids) it can't be beat. They have a Parent Swap program where adults with small children can obtain a pass to bypass a line. One parent waits with the children at the exit. After the first parent rides, the second parent may come up through the exit and get on the next available ride. You can bring one additional guest from your party to ride with you. They also have 4 nice areas for kids with rides and play areas. Kids stuff is Peanuts themed. Good point about CP is that they've lowered the admission for 2006. Bad part about CP is that they have a very nice water park in Soak City, but admission is seperate. They do sell 2 day passes, but those are actually more expensive than buying admission to each park seperately. I guess it's because you can "hop" between them for 2 days.
Geauga Lake is close to me. And IMHO not worth a 2 hour drive. We go because it's 20 minutes away. Geauga Lake and Sea World Ohio used to share a property, though they were maintained as seperate parks, seperate owners. Some years ago Six Flags bought the property from both and combined it into a Worlds of Adventure park with amusement rides, added a huge very nice water park and had maintained some of the animal shows that Sea World had. It was a very nice park with more than you could see in 2 days. Two years ago Six Flags sold the property to Cedar Fairs (owner of Cedar Point amongst others) and they closed the sea life part and simply stripped off all trademarks of Six Flags and opened up. It's boring and ugly. Last year I was hoping that they'd have made some improvements to the decor.... but nope. Still old, stipped and ugly looking. Half of the time the rides were down and many of the older water attractions (they have 2 water play areas) were not working disappointing the kids. We have not made a trip there yet as of this year, but will soon. We go because it's fairly cheap, 25 adults, 10 juniors and the Wild Water Kingdom part is really very nice. We could almost spend the whole day there. Kids enjoy the rides even though I think the place is just awful ugly atmosphere.... it's close and it's not too expensive for an amusement park. But Cedar Point is by far the better of the two and with their lowered prices, 40 adult, but we get military discount of 30 and 10 for juniors we may just take the extra hour drive and do CP more this year.
In Columbus don't miss COSI. Especially if you are a Star Wars fan. We attended the opening weekend of the Star Wars exhibit and wished we could have spent more time in the other parts of the museum. Fantastic place.