All of the hotels have character dining nights. Woody Woodpecker, Scooby Doo and Spidey are frequently there, although the line up is subject to change, as is the schedule. Ask a concierge at any of the hotels; they should be able to give you the low down on what will be on offer at all the hotels during your visit.
Also, check for a character breakfast and/or lunch at Confiscos in IOA.
Regular character appearances in Toon Lagoon (IOA), Seuss Landing (IOA) and KidZone (USF). Hollywood and TV characters often stroll on Hollywood Blvd. (USF)
My guess is that as Harry Potter gets closer to opening we'll see HP characters in the Lost Continent. But that's just a guess and a ways off.
What have I missed?