Best Westerns have pets and Extended Stay America also allows pets. They are in the chicagoland area, but not sure of any in chicago, but I think by O hare airport. I think you must have them in a cage when you are not around, especially if they have to clean the room.
I feel bad most Hotel politicizes will not allow you to keep a dog alone in the room by them self or allowing you to bring a dog to the Hotel. Do me a favor call be for going check out different hotels in the area your going to make sure so that your not disappointed.