I have seen Six String Samurai- It is okay. The set-up is great! The movie doesn't quite deliver.
A few other Post-Apoc Movies:
A Boy and His Dog- You've read the book, now see the film! Starring Don Johnson!
Children of Men- Not Nuclear, but still after a big Collapse.
28 Days/28 Weeks Later- Ack! Zombies.... kind of....
The Omega Man/I am Legend/Last Man on Earth- Again, not Nuclear.
On The Beach- Ah.... delicious Nuclear Apoc.
Threads/The Day After- More Nukes, and pretty depressing
Reign of Fire- Dragon Apocalypse!
Cherry 2000- Cheesy 80's Apoc and a USA Up-All-Night classic!
Hell comes to Frogtown- Rowdy Roddy Piper Apoc!
DefCon 4- Had a great video box cover. that's all a I recall.
Night of the Comet- 80's valley girls tweens vs. the Apoc.
Omega Doom/2019: After teh Fall of New York/2020 Texas Gladiators- 80's Cheese!
This list might help....
Enjoy. Mwahahahahahahahahahahhahahahaha! Oh... did I just laugh in a way where you could all hear me... ignore that please.