From my Trip 2 years ago....
Italy is a great place to smoke as long as you are outside. Everyone is lighting up something everywhere you go. As suggested by several here when I was in Rome, visited Fincato Cigar shop. This shop is in a good location, close to the Pantheon and the Trevi Fountain, but is a bit hard to find being obscured by some construction and down a side street.
The first floor of the shop is clearly for the standard walk-in customers and the tourist trade. I am sure the get a lot of Americans that have no idea what they are buying. They have some very low-level Cuban cigarillo-sized things down there for those that just want to say they brought home a Cuban cigar.
Frankly, they are a bit dismissive - almost rude - of anyone walking in that is clearly a tourist until they know you are serious about buying something serious. As soon as they realized I was going to be buying a couple boxes their attitude changed quite a bit! The real Cubans are kept upstairs and they call someone to meet you up there. Before I went I had checked prices on a certain PURO site that promises EXPRESS delivery of Cubans to the US and, to my surprise, on several sticks the Fincato shop was significantly less. Others were quite a bit higher and most competitive. As you might expect the price for boxes/cabinets are cheaper than singles.
Unfortunately their inventory was very low. I would have bought some more if they had had them in stock. They had been expecting a new shipment for several weeks and they had been very busy. I picked up their last box of Monty #2s, all of the loose Hoyo de Monterrey Epi #2's they had on hand (they were out of unopened boxed ones) and a handful of Party Series D's. They charge a 3% surcharge on credit cards but right next door was a bank money machine that had no fee on it so, combined with my Capital One card that doesn't charge anything and that gives you a fair rate, it worked out pretty good.
The best part was when I was first looking and the guy was acting a bit put out having to wait on this tourist and I asked if they had any unopened boxes/cabinets of the Hoyo Epis and when he said no just the open boxes in the humidor. I said if he gave me the cabinet price I would take every loose Epi he had - it was almost a full box-load and he really perked up when I said that. Suddenly I was worth being treated royally and had another guy rush from around the counter to greet me the next day when I wanted the box of Monty's