Your best opportunity to see Peter Pan is at a character Meet ‘n’ Greet in the Magic Kingdom. Currently characters from Peter Pan can be seen around the exit to the Pirates of the Caribbean attraction. The latest schedule has them there from 10 a.m. until 5:30 p.m. Check the Magic Kingdom Times Guide when you enter the park. This schedule can be found next to the park maps.
Peter Pan may appear at Cinderella’s Royal Table for breakfast and lunch but there is no guarantee. It is my experience that his visit here is very random. However dining in Cinderella’s Castle is always magical.
For another Peter Pan idea, I would consider the
Family Magic Tour at the Magic Kingdom. While the character that you meet at the end of your adventure can differ, Peter Pan seems to be there most frequently. The cost is currently $27 for ages 3 and up.
Follow up any of these ideas with a visit to
Peter Pan’s Flight in Fantasyland. Enjoy your journey - “Second to the right, and then straight on till morning”!