[Deals like this tend to expire quickly so this article may be out of date after March 19, 2016]
Kudos to theflightdeal.com for finding this deal!

American Airlines is offering an excellent deal where you can fly for under $500 from the US to Milan, Italy.  American Airlines offers one of my favorite elite programs with perks that include complimentary first class upgrades and reasonable award flight redemption rates.  You can credit the flights below to American Airlines’s or Alaska Air’s frequent flier program.  In addition, you’ll want to use a credit card–such as the Chase Sapphire Preferred, Citi Prestige, or Citi Advantage Platinum–that offers additional points for airfare purchases.

Italy requirements requirements:  U.S. citizens may enter Italy for up to 90 days for tourist or business purposes without a visa.

I used Google Flights to find exact dates and organized the screen shots by departure city.  After you find the flight that you want, I recommend booking on Orbitz so you can earn Orbitz Rewards in addition to airline miles.

Departing New York (JFK)

• Airline: American Airlines
• Destinations: Milan, Italy (MSP)
• Dates: March 2016 to May 2017
• Special requirements: it looks like a 7 day, six night stay is required for most flights
• Other notes: most flights are direct on American’s 767-300.  I recently flew this aircraft in business class from Rio de Janeiro to Miami and really enjoyed the hard product.    I have not flown this plane in economy but you can look up the seat configuration at www.seatguru.com.

From Google Flights.  Google and the Google logo are registered trademarks of Google Inc., used with permission.

Other cities

• Philadelphia (PHL): Round-trip fares are available from $598 on American Airlines (code share British Airways flight).
• Boston (BOS): with very limited availability, round-trip fares are available from $696 on American Airlines (code share with British Airways).