An affordable luxury boutique hotel? Apparently! The newly opened, 285-room Public Hotel Chicago is promoting luxurious appointments and impeccable service, along with a livable price tag. The location is a completely remodeled former Ambassador East Hotel, once and still home to the celebrity-haunted, pop culture-celebrated Pump Room restaurant. The mastermind is Ian Schrager (co-founder of the infamous Studio 54, often credited as the creator of the boutique hotel concept, that Ian Schrager). The oversize rooms feature a “soothing, ‘no palette’ color palette,” 300 thread count linen, custom and iconic hand-picked furniture, a mini-bar that you can custom stock at check-in, … the list goes on and on. The Pump Room has been reborn under acclaimed chef Jean-Georges Vongerichten, with a healthy-food, local ingredient approach to fine dining. All of this and more, with rooms starting at $135 a night…