Store pickup implies that you will be given one from their in-store stock. I doubt the NYC stores stock Italian layout keyboard computers.
Though it is entirely possible that if you order something that is not sold in the store that they will special order it for you from the warehouse and then ship it to the store where you will pick it up. That will probably take some time, though. But I am thinking you will also have to buy some sort of adapter to charge it in Italy, we don't have the same types of power outlets. Apple sells a world travel charger kit for 40 USD, but you could probably buy the individual adapter you need (continental Europe) for a lot less.
You will want to check on import and export duties, also. If Italy requires you to pay if you bring the item into the country from abroad, or the US requires you to pay to take it out of the country, the cost savings may not be worth it. Plus, you are going to have to pay some sort of currency transaction fee when you purchase the item, I am guessing. Though the Euro to US Dollar exchange rate looks favorable for you.
You could probably avoid paying any duties by just putting the computer in your luggage without the box, like if you had brought it with you from Italy to use on your trip. Which would not be an uncommon thing.
There is also the issue of warranty coverage and Applecare. It may be difficult to obtain coverage or to get repairs covered if you buy it in one country and try to get it repaired somewhere else, where the laws are different. You would want to check on that.. Even one out of warranty repair could negate any money you saved by buying it abroad.
The cost savings is roughly 500 USD, which is pretty significant. The price in the Italian Apple Store is 1829 EUR with VAT, which is 2493 USD. Your price with tax in NYC will be just under 2000 USD.
You are going to have to pay the sales tax if you buy it from an Apple Store, or even an online retailer who does significant business in NY state, but has no physical presence there (like MacMall).