The Smithsonian's railroad artifacts collection is the capable hands of Bill Withuhn, who has done a great job succeeded the towering John White. For railroad engineering and social history scholarship these guys are a powerful double threat.
The collection includes a number of engines in addition to the SR 1401 4-6-2. The Museum is about to overhaul the Railroad Hall to replace the "stuffed and mounted" approach with more interpretation. As part of this, a number of engines are going to be rotated out for display at other Museums which have been named "Smithsonian Affiliates." You can read about the whole job in the link attached.
Equipment (inlcuding engines) not on display or on loan is stored at the Museum's conservation facility in Silver Hill, MD, about 10 miles due south of Washington DC.
Generally the Silver Hill facility is not open to the public. You may be able to arrange a tour or a site pass through the Museum itself, or through your federal (not state) congressional delegation.