Well, staceyjan, it looks like we Italian jewelry enthusiasts are in the minority! Lol. I'll see if I can help you, since I have been to Italy a couple times in recent years (just not to Rome, which was why I was asking the question above about stores there).
It really depends on what city your friend is visiting. Florence is famous for its 18k gold (the Ponte Vecchio is there, which is an entire street dedicated to selling gold). There you can find pieces with the beautiful textured Florentine finish and also Buccellati-type jewelry with delicate filigree. Both are favorites of mine. I believe Venice is famous for its glass jewelry, although I haven't been there so this is just what I have read. Southern Italy has more Greek influences and that is reflected in the pieces. I went to the Amalfi Coast and Capri two years ago, and the jewelry there has brighter, bolder colors and designs. Very island-inspired. From my own research, Rome seems to have Etruscan-type designs and larger pieces with symbols, like snakes, evil eyes, and even Roman coins.
All of that being said, you can really find almost any kind of jewelry you want in Italy. The suggestions above are just what is specific to each region. To help your friend out, I would try to decide what kind of style suits you most and what type of jewelry you'd prefer. Really, you can't go wrong and it will be a wonderful piece you will cherish!
I hope some of this rambling helps. Lol.
) and totally amazing