The "between9and5" website arranges day rooms in various locations, including Berlin. We successfully used this site to obtain a room at the Hotel Lindner in June 2014. It was satisfactory in every way, with the sole possible "exception" being that we were only allowed to check in precisely at 9am, even though there was likely space at the hotel. Given our flight schedules we appeared at the front desk at 745. So, we had tea on the Ku'damm.

http://www.between9and5.com/