Places to visit

UK: 

Finch Bros  Finch Foundry - Sticklpath, Devon

A Morris & Sons - the Iron Mills, Dunsford, Devon (note this is a working factory, and you MUST not just turn without making an appointment)

Bache Bros - Churchill Forge, near Stourbridge, Worcs

Abbeydale Industrial Hamlet - Sheffield, Yorks

Shepherd Wheel - Sheffield, Yorks (grinding hull, not a forge)

Holbeam Trip Hammers - Science Museum, London

France: 

Musée du fer et de la forge, Montgailhard, Ariège (09)

Lo Martinet de la Ramonda - La Bastide-l'Évêque, Aveyron (12) 

Philibert Frères - Scythe Museum, Nans sous St Anne, Doubs (25)

Taillanderie Busillet - Marthod, Albertville, Savoie (73)

Forges et Moulins - Pinsot (between Chambèry and Grenoble), Isère,  (38)

Le Musée du Saut du Tarn - St Juèry, Tarn (81)

La Vallée des Forges - Pont Salomon, Haut Loire (43)

Taillanderie Alexis - M Bernard Solon, Orléans, Loiret (45)

Musée Historique et Industriel - Reichsoffen, Alsace (67)

Usine métallurgique - Forge de Jaegerthal, Niederbronn-les-Bains, Alsace (67)

Musée de la manufacture des armes blanches - Klingenthal, Alsace (67)

Spain:

Os Teixois - Taramundi, Galicia

Museo de la Máquina-Herramienta - Elgoibar, Gipuzkoa Basque region

Martinete de Navafria - Segovia, Castille et Léon

Switzerland:

Mulino Aino - water powered complex and museum - San Carlo, Graubünden

Forge du Martinet de Corcelles - Corcelles, Bern

Musée du fer - Vallorbes, Vaud

There are the remains of a water powered forge at the monastary at Beinwill, Solothurn, for more water mills in Switzerland see 'moulins' or Mühlefreunde (in German)

Note: some of the Hammer Forges in Spain and other countries are not edge tool works, but the principles of the machinery are the same.

If you know of other similar museums, please let me know.