There is a branch of the Chuck E Cheese restaurant chain in Appleton. We haven't been to this particular one, but I'm going to guess it's very similar to the one we have? Mascot show, game room, kids' paradise...
There's no admission fee, but the only thing you can do for free is watch the show.
Chuck E Cheese
4671 Michaels Drive ~ Appleton, WI ~ (920) 832-8323