First off, this is perhaps a pointless thread as no consensus of ANY sort will ever be reached on "what city is the coolest." That said, in order to further antagonize the title of the thread, I will throw my hat in the ring to say why something is "cool" versus why something "sucks" (Do we really need more internet threads detailing why things suck? Don't we have enough of those?).
I don't know anything about LA, NYC, FL, etc. I have visited all of these places, but I think it's true that you have to live in a place for awhile to get a feel for what it's capable of bringing to the table.
I have lived in Chicago for the last five years. I will probably be leaving it to attend law school in the fall and that is almost entirely due to the winters. They have really gotten to me, I'll admit it. It is cold and windy and it gets into your bones. However, I realize this is because I am giant wuss who hates winter and that's not the case for everyone.
If you can deal with winter, Chicago is freaking amazing. If you like a party scene there's Wrigleyville. If you are a hipster kid there's Wicker Park. If you are gay, head out to North Halsted. If you are a gay, hipster kid who likes to party, give Andersonville a try. There is literally a neighborhood for almost any conceivable ethnicity/interest/sexual preference/etc you can imagine. While many other large cities are segmented in this way, in my experience moving between them isn't as easy or as welcomed as it is in Chicago (I mean that in both the physical and social senses).
Beyond this, the music scene is underated (seriously underated), the sports facilities are fantastic, the musuems and city parks are top notch and for the 2.5 months of summer we get here, everyone lives outside: the beaches open up, everyone dines outside, bicyclists are everywhere and Michigan Ave. is packed.
It really is a great city. I won't miss the winters here, but I will miss the culture.