The Stand by Stephen King. Yes, it's a lot of post-apocalyptic novel, especially if you read the author's preferred Super Doorstop edition, but I loved having that much time to spend with all of the characters throughout the apocalypse and beyond. King lingers on the horror of it all and also puts some time into the rebuilding aspects.
Lucifer's Hammer by Larry Niven and Jerry Pournelle that shows the impact of a huge metorite on the California coast and then the attempts by the characters to survive and, if not rebuild, fortify. It's a solid read, if pessimistic and probably a bit too libertarian tinged to be really enjoyable.
For a totally goofy take on nuclear apocalypse fiction, I can't actually recommend Jerry Ahern's The Survivalist series, but I've ready a bunch of it and enjoyed it as trashy men's adventure fun. John Thomas Rourke, a sort of prepper culture Mary Sue, will do what it takes to _survive_, which gets increasingly ludicrous when later books start to involve cryogenics and fighting those goddamned commies into the distant future. It's a savage slice of Reagan-era cheese and in no way realistic, except for the loving descriptions of the firearms our heroes use gleefully kill the aforementioned commies.
However, if you're looking for something post-nuke then you should really read some of the titles already mentioned above. I enthusiastically second the following:
A Canticle for Liebowitz by Walter M. Miller Jr., about how long after the nuclear holocaust the Catholic Church attempts to interpret relics left behind by a mysterious saint. It's an absolute classic and if you read one post-apocalyptic novel this should probably be it, though it takes place well after the event itself and is about future societies interpreting the past and rebuilding based on old knowledge.
On The Beach by Nevil Shute, about a military sub that lands in Australia after the nuclear war and how everyone attempts to come to terms with impending doom. It's quietly grim and very good.
The Postman by David Brin. No, seriously, it's pretty good. After the war a survivor starts to wear a postal uniform and that brings the promise of hope of society being able to rebuild. I have no idea what the movie is like but the novel is a solid read.
While we're going post-nuke, I don't remember it terribly well but I did enjoy Alas, Babylon by Pat Frank, which I believe was a fairly early entry in the post-nuclear apocalyptic novel genre. Florida gets nuked and the folks there try to survive, though, I mean (insert Florida joke here).
I can't vouch for the whole trilogy but N.K Jemisin's Broken Earth Trilogy is award winning, acclaimed, and top notch fiction about a world that undergoes total catastrophic apocalypses on a regular enough basis that they have structures in place for how to rebuild afterward, which doesn't make it any less terrible or traumatic. The first novel, The Fifth season, was excellent but harsh enough that I haven't gotten on board for the two sequels.
Finally, books I keep meaning to read but haven't gotten around to yet are Swan Song by Robert McCammon and The Long Tomorrow by Leigh Brackett. One day!
