This isn't a character meal in the Disney sense - but twice we have been at IoA and had lunch at Circus McGurkus. It is a counter service place in Suess Landing.
They have a show with Dr. Suess characters that they put on in the middle of the restaurant (there is a schedule posted on a sign out front). Both times we've been there, after the show, all of the characters have come around to each table for autographs and pictures. It was like Thing 1 and Thing 2, Sam I Am, Green Eggs and Ham, Cat in the Hat, etc.
Anyway, they spent lots of time with my kids. I will mention that we've been there when it wasn't crowded, and we were eating early - it may not always be this way. But it was certainly easy and cheap. It's as close as my kids have ever gotten to a character meal!