During the early 1980's video stores were filled with a whole host of Post Apocalyptic movies.The most prolific output for this genre came from Italy and it seemed like a new one was released every month!
Bad dubbing,loads of violence and crazy characters always brought this fan back for more with these films.Also,like many Italian genres during this time you would see a lot of the same faces in a lot of the films as some directors made multiple films of the same style.The first 3 choices here show that as they are all directed by Enzo G.Castellari within 12 months of each other!
Here i present some of the best (or worst depending on your opinion)of these films for you starting with my favourite!

BRONX WARRIORS (1982) DIR:ENZO.G CASTELLARI
In a post-apocalyptic New York City, a policeman infiltrates the Bronx, which has become a battleground for several murderous street gangs.

BRONX WARRIORS 2 (1983) DIR:ENZO.G CASTELLARI
A vicious corporation tries to kill and starve the last remaining habitants of the Bronx in order to build their own high-rise developments.

I could'nt find a trailer for this film so instead here is an actual clip from it.

THE NEW BARBARIANS (1982) DIR:ENZO G.CASTELLARI
Two mercenaries help wandering caravans fight off an evil and aimless band of white-clad bikers after the nuclear holocuast.

2019:AFTER THE FALL OF NEW YORK (1983) DIR:SERGIO MARTINO
After a nuclear war, society breaks down into two groups, the evil Euraks and the rebel Federation. A mercenary named Parsifal is hired by the Federation to infiltrate New York City, which is controlled by the Euraks, to rescue the only fertile woman left on Earth.

2020:TEXAS GLADIATORS (1982) DIR:JOE D'AMATO
In a world where government has deteriorated...laws are unbinding...and cruel savages rule the wastelands, comes a new heroic breed... The "Rangers," a team comprising of disciplined, dedicated, and laconic mercenaries are on a mission...to exterminate the evils that roam in the post-nuclear world.

EXTERMINATORS OF THE YEAR 3000 (1983) DIR:GIULIANO CARNIMEO

The year 3000, after a nuclear war turned the earth into a desert. A group of survivors living in a cave runs out of water and desperately needs a new supply. The last person they sent out didn't return. His 10 year old son Timmy wants to join the next team. They know where they'll find a well, but the problem is the way there, which is controlled by a savage gang of motorcyclists under the bloodthirsty Crazy Bull. A lonesome stranger who Timmy meets on the way may help.

Here is a pretty long clip showing just how much the film Mad Max influenced the directors of this genre.