I've gone through a lot of the families and I'm not finding any potential connections to Jon's mother possibly being highborn. I wondered if he could be linked to the Dornish houses but the potential women candidates are thin. Same with the other nobel houses.
If a highborn women hid a pregancy and gave the kid to Ned - hiding the pregnancy would be tough. If she was already married they would've had to fake the babies death I would think.
According to some timelines I've found, Ned was 18/19 when Jon was born. Would assume a highborn mother was of the same age unless it was a house 'servant' as rumored or a whore. What are the theories - and please no spoilers.
Ned - born 264, died 298 (age 34)
Jon - born 283
I can't really get into the theories without spoilers...but the one BIG theory is that Jon isn't Ned's son, but is still a Stark who Ned took in to protect him from people who may want to do him harm based on who his parents really were, and the enemies that one of those parents had.
I really hope this theory is true, because the implications are massive.
And just in case you're wondering about this theory - and again, it's only a theory, so these probably don't count as spoilers but just in case, POSSIBLE SPOILERS AHEAD...
...one of the prevailing theories is that Jon is the son of Lyssa Stark, Ned's sister, and Rhaegar Targaeryen, the son of the Mad King. Lyssa was Robert Baratheon's one true love, as you might remember, and he's also the one who killed Rhaegar's father to claim the throne for himself. So you can see why this would complicate things for little Jon, and why it makes sense that Ned would take him under his protection and raise him as his own, without ever getting into who his mother actually was. It also seems to be the only way Ned would ever have a "b astar d" of his own, since he was clearly not the type of man to have an affair. This also means that Jon is part Targaeryen, if true, which is why a lot of people think it'll ultimately be Jon who "wins" the Game of Thrones since he quite possibly ties the Starks and Targaeryen houses together through his lineage.
Again, this is all speculation, not a single shred of it is backed up by anything in the books...yet.