Cafe Mickey at the Ambassador Hotel has a character buffet, and so does the Horizon Bay Restaurant at Tokyo DisneySea (though it's more like a buffeteria). The Crystal Palace Restaurant at Tokyo Disneyland is another choice (for breakfast only) and probably the most elegant out of the three.
In addition to the comments above by TDR_Fan, they did do a character breakfast at the Queen of Heart's Restaurant for sometime but I believe that may no longer be the case. I would have to check.
Over at TDS, you can enjoy "Donald's Boat Builders" show while eating at the Cape Cod restaurant. The show plays throughout the day, with small intermissions.
Also, during TDS' A la Carte event, there were chances of seeing some characters in some restaurants..like Genie at the Casbah Food Court. But that event ends today.