For Mexican handcrafts enthusiasts, one must-see museum is the Franz Mayer, located on the northwest corner of the historic center of Mexico City.
Interestingly enough, it is not a handcrafts museum per se (like the nearby Museo de Arte Popular). Instead it specializes in decorative arts, mostly from Mexico but there are pieces from other parts of the world as well.
The museum’s origin is with the personal collection of German immigrant Franz Mayer. From about 1925 to 1975, Mayer collected art, books, furniture, ceramics, textiles and more dating from the 15th to 20th centuries. A significant portion of the collection is Mexican handcrafted items, and the collection is important because it contains examples of many things which have not survived otherwise because people at the time did not consider them worthy of preservation. One particular example of this are the Talavera pieces he began collecting in the 1920s, long before having the value they do today.
The musuem proper was opened in 1986, and while it does make new acquisitions, the vast majority of the permanent collection is still that put together by Franz Mayer, with only a quarter of the collection put on display at any time for reasons of space.
One particular distinction of this collection is that the vast majority is fine handcrafts, including pieces made from precious metals. However, the museum does not stop with curating this collection, it also sponsors research into Mexican handcrafts, collaborating with noted names in this field such as Marta Turok. It also sponsors temporary exhibits (which includes those dedicated to handcrafrts), workshops and presentations of an academic nature.
The museum has a website in English as well at http://ingles.franzmayer.org.mx/