The Windy City is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

When you planeswalk here and at the beginning of your upkeep, put a flying counter on target nontoken creature you control without flying. Whenever chaos ensues, exile target creature with flying. For as long as it remains exiled, its owner may cast it by paying rather than paying its mana cost. When you planeswalk away from The Windy City, remove all flying counters from all creatures.