The Lift of Florence
The start of the video is about the lift of Florence. If you have the Wall Runner perk you can get on top of the structure. Obviously if your pursuer has throwing knives or a gun they can waste you, but if they dont it can be very fun watching them trying to get you and failing over and over.
A neat stunt I have is to hang off the edge and drop a smoke bomb from above on your pursuer before he gets on the lift, then drop down and stun them, looks stylish.
Anyway as for the rest of the video, I like to try use throwing knives to stun my pursuer. Note they can kill you, but if you use mute there is nothing they can do. Use it far away from them so they cant use smoke bomb, once you get good with it you can stun anyone, but note its a very unorthodox and inefficient way of stunning, try it out if you just want to have fun.
Your right about it looking stylish. 
One thing I really like is when your target jumps off a building and lands in front of you (obviously they don't know you're their pursuer), kind of like a stunt in reverse.
Your right about it looking stylish.
This happened to me twice today. It makes you feel like such a badass. When you look up, see them leap from a building, target in mid-air, and wait...SURPRISE! So gratifying.
I can't help but feel bad for them, though. "HAHA! I got away! All I have to do is run around that corner--..."