I really want to find out more about Arthur Dayne. Everyone who talks about him says he's the best knight they ever saw. He's probably my favorite character from the past. I would also like a larger, unbiased view on Rhaegar.
I think from what we know, Rhaegar was pretty awesome. The only person who really seemed to dislike him was Robert, and it's easy to see why.
The parts I want know are regard the changes he would have made if he were king and/or if the Tourney at Harenhall was an uprising attempt.
Tormund Giantsbane or Dolorous Edd Tollett. There's enough bad-ass to go around with the main characters, and it's very hard to make someone laugh in a book. But god damn it if Tormund and Edd don't make me laugh frequently.