Here’s a few of my recommendations - old and new - grouped by Pre/During - Mostly Post and Long-Past Apocalyptic, with some dystopian stuff thrown in for fun.
Pre/During Apocalypse
The Last Policeman - Winters, Ben H. - Technically pre-apocalyptic, as an asteroid is due to hit Earth in a matter of months - a detective story set in a society slowly breaking down. The ending felt a bit off, like Winters decided at some point to make it a series, but still enjoyable. (FYI - the Kindle version is currently available for cheap!)
Slow Apocalypse - John Varley. Mostly set during the apocalypse, it’s not Varley’s best, but still an interesting take on societal breakdown. Be prepared for a tour of the greater Los Angeles area… 
*Ashfall *- Mike Mullin. The Yellowstone supervolcano goes kaboom & the teen protagonist crosses the midwest to find his family. Young-adult-ish, but still quite good.
*Sleepless *- Charlie Huston - Humans are suffering from a plague of insomnia and civilization is falling apart. A detective thriller, similar to The Last Policeman.
Mostly Post- Apocalypse
*Boneshaker *- Cherie Priest - Zombies & steampunk; perhaps more alt-history than post-apocalyptic, but - a fun read!
Zone One - Colson Whitehead. PA+zombies, which you might be a bit tired of, but it’s the most literary example of the genre I’ve read.
Warm Bodies - Isaac Marion - mostly zombie (sentient - protagonist is a Zed), some PA - dry humour and a love story, but not too sappy.
*World Made by Hand *- James Howard Kunstler. About 1 generation after a slow decline of civilization - climate change/the end of oil. I could have done without the supernatural elements, but really enjoyed the world-building.
The Maze Runner series - James Dashner. A bit of a rip-off of The Hunger Games, (kids being manipulated with deadly results) but the first novel is more or less worth reading. Some interesting world building, but the characters are meh.
The Windup Girl - Paolo Bacigalupi - First world vs third world in a hunt for foodstuffs; one of the main characters is an “engineered being” cast off by her owner & trying to survive. Bleak story, but fascinating world building. Some similarities to Oryx & Crake, I suppose.
Long Past Apocalypse
Eternity Road - Jack McDevitt. Rebuilt semi-primitive society; explorers go to find the secrets of their ancestors.
Shades of Grey - Jasper Fforde. This one is really quirky - human society is hierarchical based on one’s perception of color. Leans dystopian, but Something Happened to cause the color blindness, so am throwing it in here.