Hi Steve,
Does your wife favor Gold or Sterling Silver?
As you may know, Gold is still relatively high in price. You can find some beautiful, intricate Sterling Silver pieces in jewelry shops.
No need to haggle as if you were in an open market. You "could" ask the jeweler if they "can do better with price" if it is really something your wife loves. They may offer a 10- to 15% discount.
Rome has many jewelry stores too.
With Florence, you will see a sea of jewelry stores on the Ponte Vecchio. Most of them will be high priced.
There is a store owned by an American woman, Traci. Her place looks like a cute 'corner store.' Her things are fairly unique, vary in price. She and her staff get rave reviews.
Here she is in Firenze
https://it-it.facebook.com/goldcornerbytraci/?ref=page_internal
http://www.goldcorner.it/
Piazza Santa Croce, 15 R (6383,29 km)
50122 Firenze
Tel. +39 055 241971