I have been thinking about this alot lately, first respond to TK then add my thoughts.
Maybe:
He will meet the 3-eyed crow. I agree
He will meet his uncle. I agree
He will connect with Arya through his Green Dreams. I am of the belief that this will not happen until Arya regains her sight, and even so depends how much of herself she loses becoming a faceless.
He will wake the Children of the Forest. I am not sure they need awakening so to speak, but there will definately be interaction.
He will lead the Wildlings into the Gift. Will Jon allow it? A Bran v. Jon scenario perhaps?
He will rebuild Winterfell. He is the current heir, and I would like to see this happen.
We will be the true knight he always wanted to be. Similar to Aegon's comment but I believe he will surpass mere knighthood.
Bran I believe will be a major player in the fight against winter. I am confident he will be involved that if Jon and Benjen meet again it will hinge on Bran. I do not think Coldhands is Benjen, but more likely an ambassador for or an actual child of the forest. Osha had said while talking with Bran that children are still beyond the wall, and his talents for warging et al would likely be known by them, especially considering that there was a godswood in Winterfell that would allow them to "watch".
I think my interest in Bran is that I do not believe the dragon's are the solution to the others. The other's are not effected by fire, although the wights are, so fire isnt an effective tool for them. Granted the dragon's could burn swaths of forest but that would weaken the children. The dragons birth, in its use against winter, I propose is the parallel rebirth of magic. The candle in oldtown, Bran soon to meet Coldhands, and the awakening or strengthening of the children all coincide. The old ways will be needed to defeat winter, where as the dragons will be needed to conquer Westeros.
The three parts that I'm most curious about the battle with winter hinge on whether the wall falls. The others cant get around from the old magic in its construction. If the believed horn of winter is in oldtown, how do they manage to bring it down? If it does fall does winter finally lose again at Winterfell, or rather its ruins (if im correct the exterior walls are still standing)? And what role do the children on God's eye play?
Any thoughts?