I'm new and am loving reading everyone's thoughts in this thread!
The Brooklyn neighborhood I live in has for a number of years been practically synonymous with "cool" - but a self-conscious type of cool, to the extent that I think it's come full circle and the coolest of the cool have moved on.
The common thread of coolness here is less what is the outfit? and more how well is the wearer pulling it off? Every season I see people wearing basically the same components, but some, of course, look miles better than others. I hate to admit it, and I wish it were otherwise, but all too often body type plays into how cool a look reads. It's easier to pull off contemporary looks with a tall, lean body type, and many locals with that body type take full advantage of it by wearing maximally trendy outfits. Sometimes it works and often it doesn't, but they have a better chance of pulling it off than many others.
A certain marginally-unwashed nonchalance also contributes to looking cool. Think of the members of any guitar band that plays in trendy bars that claim to be dives but serve $17 cocktails - that slightly dirty hair/not-so-fresh t-shirt look. Everyone here wants to look stylishly undone without tipping into full-on grubby. Overly "done" hair or a "trying too hard" full face of makeup doesn't look cool. This can be frustrating because, again, it's up to genetics - if someone suffers from bad acne, it's not cool to walk around barefaced, but possibly less cool to use enough makeup to cover it up!
Rock and a hard place - that's coolness to me. Even the coolest never really feel like they're quite there. Anyone who's totally confident about themselves is more likely a fabulous eccentric than a "cool kid."