Here are some quotes from AGOT where Jon reflects on his mother:
Jon’s anger flared. “He said my mother was—“
“—a whore. I heard him. What of it?”
“Lord Eddard Stark was not a man to sleep with whores,” Jon said icily. “His honor—“
“—did not prevent him from fathering a bastard. Did it?”
"Words won't make your mother a whore. She was what she was, and nothing Toad says can change that. You know, we have men on the Wall whose mothers were whores.
Not my mother, Jon thought stubbornly. He knew nothing of his mother; Eddard Stark would not talk of her. Yet he dreamed of her at times, so often that he could almost see her face. In his dreams, she was beautiful, and highborn, and her eyes were kind. (Jon III, AGOT)
There was no place for him in Winterfell, no place in King’s Landing either. Even his own mother had not had a place for him. The thought of her made him sad. He wondered who she had been, what she had looked like, why his father had left her. Because she was a whore or an adulteress, fool. Something dark and dishonorable, or else why was Lord Eddard too ashamed to speak of her? (Jon V, AGOT)
It would be good to see Arya’s grin again and to talk with his father. I will ask him about my mother, he resolved. I am a man now, it is past time he told me. Even if she was a whore, I don’t care, I want to know.
How could they think his father was a traitor, had they all gone mad? Lord Eddard Stark would never dishonor himself . . . would he?
He fathered a bastard, a small voice whispered inside him. Where was the honor in that? And your mother, what of her? He will not even speak her name. (Jon VII, AGOT)
He wanted to say that Lord Eddard would never dishonor himself, not even for love, yet inside a small sly voice whispered, He fathered a bastard, where was the honor in that? And your mother, what of his duty to her, he will not even say her name. (Jon VIII, AGOT)