As is customary of older anime, be aware most if not all of these contain any of the following: graphic violence, graphic nudity, high amounts of foul language. In other words, its probably not for your grandma or your living room TV.

Bubblegum Crisis (DO NOT start with Tokyo 2040, start with the original OVA first, it has better aesthetics and art) is always a recommendation from me. Along with the related series Bubblegum Crash, AD Police Files, Parasite Dolls, and A.D. Police: To Protect and Serve.

Armitage III has a cyberpunk aesthetic but on Mars, the story isn't perfect but it's interesting enough. The original, not the movie with Kiefer Sutherland which is just the OVAs cut down into a movie.

Dominion Tank Police was a fun series.

Goku Midnight Eye is all attitude and little substance. I really liked it, but don't watch it expecting an intricate plot. Its just entertainment, not more. But its cool entertainment.

Cyber City Oedo 808 is another one that isnt that deep but oozes pure classic cyberpunkium.