Ned Stark has five legitimate children (in order of age) Robb, Sansa, Arya, Bran, and Rickon. Up through the events of A Dance With Dragons we end up with the following:
Robb - dead
Sansa - Alive, at the Eyrie, under the protection of Littlefinger who is plotting something.
Arya - Alive, off in Bravos, but even if she does return would still be behind all the others.
Bran - Alive, may or may not return, but given his situation it highly unlikely he would be laying a claim.
Rickon - Alive, MIA (Davos has been sent to see if he is hiding on Skagos)
Sansa and Rickon would have the best claims based on the above information. This would also mean that the Boltons will have to be stripped of their titles over the North as well. I do not see this as a major problem as the other Lords of the North believe only a Stark can rule Winterfell.
Sansa seems to be in a position to claim sooner, but Rickon is liable to just pop out of nowhere (much like Aegon VI). Littlefinger will not have wanted all his hard work to go to waste, so I would imagine he will do anything to install Sansa. The other Lords of the North may back Rickon as he is male... given the general rules of succession in Westeros, male heirs are given priority over females. However, with the state of turmoil most of these rules are subject to all kinds of interpretations and ignorance.
However, there is final option... Jon Snow. If Jon was able to secure a royal decree making him a true Stark his claim would be better than both Sansa (Jon is male) and Rickon (Jon is older). Is there any evidence that this has happened?
I am looking for evidence from the books only. The show is outpacing and has gone in different directions in many instances.