I have heard there is a museum in the works in the USA and I hope to be a part of it but from what I have seen so far…
The best faceting museums are in europe
France – A great museum with machines from the 1800s
http://www.juramusees.fr/sites/des-metiers-et-des-hommes/maison-du-lapidaire/
Czech- I haven’t been here yet but the photos look amazing
Germany- several good ones in Idar, first one is incredible. a cutting mill from the 1700s
http://www.edelsteinminen-idar-oberstein.de/die-weiherschleife.html
http://www.deutsches-mineralienmuseum.de
http://www.edelsteinmuseum.de
Netherlands- Diamond Museum
http://divaantwerp.be/en/
Also related, I heard about a museum in Rhode Island that is not faceting but old fashion die cast silversmithing and goldsmithing. So cool.