Many good suggestions here, with Fallout series being my favourites too. As HeathGCF already said, Dying Light is an excellent game, underrated I would say. Dead Island is similar, more like a precursor.
My understanding is that you're more interested in apocalyptic/survival games with some base management in them, so Dead State: Reanimated, Project Zomboid and Judgment: Apocalypse Survival Simulation are probably the ones to look at.
Not sure if it fits the apocalyptic category, but RimWorld is another very good game, with lots of management.
Some other interesting games, that could technically be considered post-apocalyptic, are the ones made by Big Robot. I personally enjoyed The Signal From Tolva (give the Lorebook a read if you'll play it) and Sir, You Are Being Hunted is good too. Their latest one, which is in early access,
The Light Keeps Us Safe looks and seems quite good, so maybe keep an eye on its release. Hopefully it will come to GOG too, since their other games are here.