I love this genre too and the type of hero you described is my favourite!
Lovers definitely fits what you're looking for 100%.
It has an amazingly sexy male lead who is totally badass! Wicked fight scenes and a really sexy romance. I can not guarantee that how the story is put together will be to your liking, but trust me when I say it's exactly up your alley in terms of what you've described here. The only requirement of yours that it doesn't meet is that it is from 2006, but it doesn't look dated at all. If you didn't know it was released in '06 you could have easily thought it was from more recent years.
Also I haven't watched them yet myself but I've been told Rondo and Time Between Dog & Wolf are somewhat similar to Cruel City, esp the latter.
If you're up for movies, try I Saw The Devil, A Bittersweet Life, Nameless Gangster, A Better Tomorrow. The leads in these are all criminally hot! If you don't mind less attractive ahjussi male leads, give Old Boy a go if you haven't yet seen it. It's a classic.