Z for Zachariah by R.C. O'Brien was a hit for me and it checks all the boxes of what you're looking for.
Here is a summary from GoodReads:
A gripping, thought-provoking story about life after a nuclear holocaust, by a Newbery Medalist. Ann Burden is sixteen years old and completely alone. The world as she once knew it is gone, ravaged by a nuclear war that has taken everyone from her. For the past year, she has lived in a remote valley with no evidence of any other survivors. But the smoke from a distant campfire shatters Ann's solitude. Someone else is still alive and making his way toward the valley. Who is this man? What does he want? Can he be trusted? Both excited and terrified, Ann soon realizes there may be worse things than being the last person on Earth.
Though the summary doesn't do it justice, it really is an outstanding novel. (It also doesn't have much violence and the little that is included is brought about when the characters are pushed to their very limit, so no pointless violence . )