The Buckingham Athletic Club is a great hotel. It is part of the Chicago Board of Trade new building. I have stayed there three times.
The hotel occupies the 40th floor of the building and has amazing views. You check in at the security desk at the lobby. There are only about 20 rooms, so it feels like a boutique hotel. Staff has always been very nice and the breakfast in the athletic club on the 3rd floor is very good.
I prefer the south facing rooms as you get a great view of the Amtrak and Metra train yards, as well as the Rock Island Metra station just below the hotel. There is also a lounge with the same view.
As great as the hotel is, there are a few caveats. It can feel a little weird going in an otherwise empty office building at night and on the weekends. The keys are very bulky (they include a security card), but you can leave the keys at the security desk / check in when you are out. You have to take two elevators to get to the hotel rooms (one to the 39th floor, and a second to the 40th floor). Also, being in the south loop there is not much in the nearby area in terms of restaurants, etc.