I wasn't able to find definitive sources, so this is my own read of the lyrics:
As you mentioned most of the song is straightforward, and seemingly autobiographical. It recounts the road-weariness of a touring singer, as he travels from town-to-town.
You can think about the woman or the girl you knew the night before
This line is ambiguous--it might be about two separate people, a woman and a girl, and it might be about many people--a stream of one-night stands. But I think the most natural read is that this is about one person, probably a fan he had a sexual encounter with in a previous town. He first calls her a woman, and then adapts that to "girl." That hopefully doesn't mean she's actually underage, but that he sees her as young and relatively unseasoned by life.
Even assuming the character in the song is a singular person, however, she's probably a composite figure, drawn by the songwriter from several real-life models.
Rememberin' what she said
Again, this is ambiguous. One possible read is that this is a character not referenced elsewhere in the song, perhaps someone important to him who is always on his mind. Another read is that she's the small-minded person who said "is that a woman, or a man?" when she saw the presumably long-haired rock singer come into the restaurant. But I think the most natural read is he's still thinking about the girl from the previous night.
In sum, I think he had a one-night stand with a fan in a small town. As a touring artist, he can't form permanent relationships, and doesn't expect to see her again. But she stays on his mind, and having to leave her contributes to his road-weariness. It all goes along well with the theme of the song, that he has to "turn the page" and start over fresh each time he hits a new location on his tour.