Michael,
So many choices, so little time!
I think that with a 13-year old it is great to take them to something that is not focused on Disney characters, but instead offers them some alternative fun more targeted at their interests.
One that might not hit your radar is the Sunday Gospel Brunch at the
House of Blues at Downtown Disney. This rock and roll themed venue will give them some distractions and entertainment that plays more to a teen than the traditional character meal might.
Another choice you might not expect, but that I would recommend, is going to the
Biergarten in the Epcot World Showcase for dinner, when they have beer-hall style entertainment.
As to more traditional character dining, I would say that
Mickey's Backyard BBQ would be a good choice, or the
Spirit of Aloha Show at the Polynesian. The BBQ is a great outdoor setting with live entertainment, and the Aloha show has such a fun luau vibe that it is entertaining to all ages.
I am glad to answer any other follow-up questions that you may have. Just go to my bio page to ask!
Have a magical (and delicious) vacation!