From our recent trip to Rome and the Amalfi Coast...
Gelato
In Rome, Carapina. This is a small Italian chain that (I believe) originated in Florence. We ate at the location just south of the Pantheon. They only have maybe 10 flavors, and they are kept in stainless steel tins that are covered (from what I understand, that is a hallmark of true artisanal gelato). Very fresh, simple ingredients, but without the fillers, it does tend to melt easier. It also isn't as creamy as you might expect (but still infinitely better than anything here in the US). We had mint (made with fresh mint, not any sort of extract, and it's not died green, either!), chocolate, and peanut (not peanut butter!). The mint and peanut were outstanding. The place I heard about over and over was Fatamorgana, but the locations weren't very convenient to our apartment, so we didn't stop there. Multiple people told us it is fantastic, though.
In Sorrento, Raki. Unbelievably good gelato! We ate here twice. I can't say enough about the pineapple basil, vanilla ginger, and cinnamon. Believe me when I say that pineapple gelato is better than a Dole Whip (blasphemy, I know!) If you get a pineapple flavor, don't mix it with anything. The flavor is so delicate, anything else just overwhelms it. We could not get past these three flavors at Raki. The flavors here are also more limited (maybe 20 at most), change regularly, and are kept in covered tins.
In Florence, My Sugar and Edoardo. My Sugar is near the Accademia. It's one of Florence's newest artisanal gelato shops, and it won this year's gelato festival. Although it's a very tough contest, I think the lime sage I had here was my absolute favorite flavor on the entire trip. If you like make-your-lips-pucker sour, then this is for you! My Sugar does not use the covered tins, but this is true artisanal gelato. We also had pineapple ginger and dark chocolate; there were maybe 20 choices all total. I liked the pineapple basil at Raki better. Edoardo is special because they make their own cones (right in front of you!), and they are oh-so-yummy! The gelato here is also in covered tins, and likewise, they have a small selection that changes daily (maybe 10-15 flavors). The cherry was very good (and the only place on the entire trip where I saw true cherry gelato; usually the flavor was vanilla with a cherry pie filling-type swirl), as was the cinnamon. We also had the dark chocolate (honestly, I couldn't really tell much difference from one dark chocolate to another).
We had gelato in Amalfi that was good, but I don't remember the exact name of the place. It is on/near the main square and had the word royal (or maybe royale) in the name. The coconut flavor here was very good (for coconut).
As far as food goes, we only had a couple of "write-home" meals on our own time. One was at O' Parrucchiano in Sorrento. This restaurant is owned by the same people/family as the hotel. It is just such a beautiful setting that you have to eat here! We had fried squash blossoms stuffed with cheese, lasagna (with little Italian sausage meatballs and eggplant), and a three pasta sampler (gnocchi, cannelloni, and something that I can't remember...ravioli, maybe?). It was delicious.
In Florence, we ate at Acqua al 2. Technically, this is a chain, as there are also restaurants in DC and California (San Fran, maybe, or San Diego?). However, we went for a specific purpose...the filet. Specifically the filet with a blueberry-balsamic reduction. It sounds weird, but it was delicious! My JA had the filet with just a plain balsamic reduction (no blueberry), which did taste different and equally good. Although there were clearly a lot of tourists eating here (mostly American and Asian - I doubt there were any Italians in the place), the menu is only in Italian, and the steak was very good, especially since, other than cured meats, we had not had much protein on the trip. Frankly, a nice steak was a real treat at that point in our trip.