The Kimpton Hotel Group runs this place. If you're not familiar with them, get to know them. All their properties are very nice and Hotel Burnham is no exception.
It's a great renovation of a classic downtown Chicago office building. It's incredibly charming and doesn't fit your normal Marriott/Hilton/Hyatt property mold.
Staff is great, rooms and nicely decorated and very comfortable.
Location is definitely the best. You're across the street from Marshall Fields (Macy's) and a 1 block walk from a major "El" stop where you can catch any of the trains. Beyond that you have all the shopping on State St and an easy walk to Michigan Ave.
The only downer, hardwired internet only (no wireless) and it's pretty slow. Faster than dial-up but not by much. And that was the case during my entire week stay.
Other than that, book it!