Bran would still be walking, the assassin never would've attacked, Tyrion wouldn't have been put into custody and there'd be no war in Riverrun, and maybe Jaime wouldn't have killed some of Stark's men and smurfed up Ned. Not sure how many things would've changed if Tyrion was in King's Landing at the time all of this was happening. Ned probably still would've gotten his head chopped off.