The first attraction that has to mentioned when talking about attractions in Seoul is the Everland Resort. The best thing about this resort is that it can fit children starting from 2 years old with its Zoo and shows, up to parents who still enjoys amusement parks themselves. 

Another Children attraction is the Children's Grand Park (The site is in Korean), but suitable for young children only. I believe that parents can find it a bit boring, as well as older children.

Another park to mentioned is Lotte world, which supposed to be indoor, but haven't got the chance to visit, Two parks were enough... 

Seoul isn't all about theme parks :)

Toksugung palace is a beautiful place to hang around, letting your kids to take out some energy. For your interests you can find a an art museum over there.

Another cool place that I can think about, which can interesting for children is the Seoul tower, where you can get a nice view of the city from above.  

Hope you'll find it helpful.