Direwolf: actually, it's not entirely clear whether a legitimised ******* comes before full-blood siblings in succession, absent any explicit naming as heir. Read the Sworn Sword to see how messy things can get when bastards are legitimised.
In any case, if Robb named Jon as his heir, it is not a simple matter. Robb's legitimisation is only valid in the Kingdom or the North and the Riverlands, to say nothing of the fact that none of the other kings even recognise that there is any crown for Jon to inherit. And Jon is a member of the NW. For all Robb's confidence, there are few precedents for releasing a sworn brother from his vows. (It doesn't help that Jon is now Lord Commander. He's pretty much irreplaceable.)
I don't actually think that Jon will accept his brother's wishes anyway. The NW serves the Seven Kingdoms, not just the North, and Jon swore to protect all those kingdoms. He has already turned Stannis down, and that was before he was made LC.
Culhwch: I don't think it follows from the fact that Stannis rejected the Targaryen claim that he is only after the crown out of selfishness. Rather, I think it's a case of not compounding the issue. He chose Robert not only over Aerys, but also over Viserys and Dany. When Aerys and Rhaegar were dead, Stannis did not insist that the crown go to Viserys, did he?
Dany has as much of claim now, in terms of right rather than might, as Viserys ever did. And in terms of right, well, Stannis knows by now that Viserys is dead and yet he has not declared for Dany. Why should he do so purely because she turns up with an army, and with dragons? Renly's army didn't make any difference to Stannis, did it?
Stannis chose Robert, and that was more to him than a matter of political convenience. It was a fundamental shift in his beliefs of what was right. In choosing Robert, he recognised Robert's line as the legitimate rulers. He stuck to that even when he was (or thought he was) behind Joff and Tommen in the line of succession, and unlikely ever to be King. So to claim that he now sticks to it only out of self-interest seems to me unfair and unlikely. Switching back to supporting Dany would seem to me to be the unprincipled choice.