I still struggle with feeling awkward as a solo diner and that definitely affects my choices. I'm pretty much there to have a decent, relaxing meal and don't need a lot of interaction with the server. I would never consider anything like Biergarten or a character meal solo. That said, I like:
Magic Kingdom
-Liberty Tree Tavern for lunch-not a character meal and the servers don't mess with you.
-Jungle Skipper for dinner-could do without the joking but the food is more to my taste. Solo seating can sometimes be awkward here if you get stuck between two large parties.