It depends on if you're into animations or not, I'm well aware that it doesn't float everybody's boat, and I wouldn't want it too, hell I think it's too popular already and am contemplating going over and starting to watch Finnish comedy subtitled instead.
But that aside I can make a few gentle suggestions... ish
As far as post apoc, there's one that comes to mind that's recent, however it's more of a drama than an action show.
Aoi hitomi no shoujo, otherwise titled The Third, the world's been blown to a giant desert pretty much, genetic critters from the world war are all around and attack human settlements and have become something of the new wildlife of the wastes.
There are those that can interface with old world technology called the third, they are marked by a characteristic red eye in their forehead, a genetic implant for interfacing with technology directly or a random mutation, it is uncertain why they exist but they do and they rule over the normal humans as protectors of the deadly secrets from the last world war.
Most of the old technology is banned, some of it is allowed so that the people can protect themselves but anything the third deem 'too dangerous for the unenlightened' are dragged off and jailed, more serious offenders have an AI construct sent after them called 'Blue Breaker', it's only used for the most dire of offenders.
Another would be Fist of the north star, it's somewhat strange, and gory, they're re-making it actually, it's another post apoc that the main character is one of the only people who decides to stand against a tyrannical conquerer that has began taking over.
The main character's fighting methods are questionable at best, he fights using pressure points and in doing so, they wind up bursting like an overripe grapefruit, personally I'd prefer a gun meself, but it's not my story after all.
A technical post apoc called Megazone 2-3 is actually a 3 movie series, it takes place in an idyllic, mid-80's city or so the inhabitants think. In reality they're aboard a large colony ship that's set to wander through space without any real direction due to the fact that the humans destroyed their world due to war and pollution.
The goal of the ship's AI is to determine if the Humans are worthy of a second chance, if they are worthy to go back to the planet after the life cycles have restored themselves on the planet of their birth.
Shin getter robo is another post apoc set in the Getter Robo Universe where professor Saotome has gone insane from Getter Radiation and attempts to build the ultimate Getter, along with resurrect his dead son.
Unbeknown to the professor, invaders seeking the Getter radiation as a source of constant evolution, survived after the original attack against earth failed when the Humans mass produced Getter Robos to be able to combat the invaders.
In humanity's panic to stop the now insane Saotome they dump a large tactical nuclear weapon on the robot he's working on, however the robot's self preservation, either an AI or the Getter itself acting within the shell, fights back and in the chaos caused by the nuclear strike and the getter beam from the robot causes Getter radiation to explode across the earth, causing the forced evolution of anything that was exposed to open air, creating a whole slew of new invaders and at the same time killing off most of the planet's natural life and vegetation.
Anyhee, that oughtta be enough for you for a bit if you're actually interested, otherwise meh, someone else might pick up on it.
P.S. Sorry for the de-rail...
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