A wonderful museum to visit, while not entirely jewellery related is
The Opificio delle Pietre Dure Museum Florence.
Do a google on this, it is usually not very busy so easy to get
tickets for it (and you can get tickets there for other Florence
attractions whose own lines are really really long)
The museum goes back to the Renaissance and is all about the art of
stone inlay to make pictures. Totally amazing stuff. There is also
the workshop were the pieces were made originally.