Firstly, a list of Must-See Medical Museums in the US:
http://culturemedicinepsychiatry.com/2014/07/22/news-must-see-medical-museums-in-the-usa/
There are surely more, including the New York Academy of Medicine, where the library often has exhibits, though mostly
online at the moment. There is also the
Beautiful Science permanent exhibition at the Dibner Hall of the History of Science.
Atlas Obscura can provide some other interesting places a little further off the beaten path and all around the world. I have a couple off the top of my head to see in Europe:
London, UK: The Wellcome Collection
Edinburgh, UK: The Hunterian
Leiden, The Netherlands: The Boerhaave
Budapest, Hungary: The Semmelweis Museum
Florence, Italy: The Museo Galileo and La Specola
and for more in Italy see
Anatomia Italia