The National Institutes of Health has a pretty large medical history collection, but you can’t see anything of it in any designated exhibition area. However, parts of the collection is on display in showcases around the huge NIH campus.
Here, for example, is a Varian A-60 NMR machine which was used at NIH in the 1960s on display in the lobby of the Natcher Conference Center (I asked historian of medicine David Cantor at NLM to pose as the fascinated spectator when we went for lunch last Monday):
(Btw, there is a lot of good info about NMR and the Varian A-60 on this site)
The NIH Museum displays some of their stuff around campus because they don’t have any designated exhibition space. But one can of course also make a virtue out of necessity — for example, I guess we could (with the right funding!) increase the visibility of the history contemporary biomedicine by placing selected objects in University of Copenhagen faculty and hospital buildings.
And if so, I guess it could be done somewhat more inspiring to the aesthetic senses than this particular Varian A-60 showcase. Even David who otherwise works in mid-20th century history of clinical medicine looked quite unexcited.