In the books, when Jon is mulling over Stannis' offer of Winterfell and legitimization, Jon admits to himself that what he wants most of all is to preside over Winterfell with a spouse and kids of his own that look like and he would name after his siblings. I think he sublimated that desire because he thought it was something he could never have. But that is what he wants most of all....a loving family of his own that he could nurture and a place where he could finally indisputably belong. I could totally see him raising a bunch of kickass little girls that would be just like Lyanna Mormont that he would teach to fight.
Given how loving he always was towards his younger siblings, I think he'd be an amazing father. I know none of this will ever happen though I feel he deserves it so much. When we're first introduced to him in the story, one of the very first things he does is sacrifice his feelings so his siblings could have the direwolves. I knew then I would love him forever. That is essentially what he's about at his core....family and sacrifice. But he has tragic hero written all over him, so he will never know nice things in his short life. He was born to suffer, save people and sacrifice himself for others. *sigh*