I can tell you that my six year old son (a VERY social only child who loves nothing more than being with other kids) LOVES LOVES LOVES going to the Kid's Clubs at Disney World. We always let him go at least one night, and he always is begging us to come back later when we show up to get him. He also begs to go back another night...which we sometimes agree to. The one at the Poly is his favorite, but he also really enjoys the one at the Beach Club. You do not have to be a resort guest to use the Kids Clubs, but you should make reservations because they do sometimes fill up.
Other opportunities for "kid" time are the different kids Pirate Cruises and the Wonderland Tea Party. Those are kid only events....and I think they run about $30 these days. My son has done all the cruises and the Tea Party and loves them all! These spots are filled quickly, so early reservations are important. If you want more information about those, let me know.