I try to bring back lightweight, uniquely Italian things. I skip the Olive oil and wine because you can buy it here. Total Wine has an excellent variety of imported wines under the Alfio Moriconi label. I actually had the pleasure of meeting this lovely Italian man!
In Venice: Light weight earrings made from Venetian Glass. I LOVE mine, and have been wearing them for ten years.
Pinnocchio Marionettes for the grandkids. (Make sure they're made in Italy)
In Florence: San Lorenzo Leather Market: Leather gloves -- you can even buy purple if you want! Embossed
leather waste baskets that are purchased folded flat that you 'open up' when you get home.
My friends all loved them and put them in their powder rooms!
Beautiful paper, letter openers for the men. Also gloves
In Rome: Campo di Fiori -- dehydrated mushrooms, bruschetta spreads,
Vatican: Rosaries for the Catholic friends, Vatican Postage stamps (It's a Country, separate
from Italy, and some people collect)
It all depends on your recipients of course, but I haven't had any complaints except from my VERY tall son, whose
silk tie wasn't long enough for him, even though I bought it in a "tall" shop and bought the longest one in there!