Flight to which Milan airport to travel to Cinque Terre

LIN is Milan's city airport. It handles only European flights.
If you fly directly non stop from NYC, then Milan Malpensa (MXP) is the only choice.
You can fly to LIN only via another European hub, such as London LHR, Paris CDG, Frankfurt FRA etc.
It is irrelevant which airport you use. LIN is really close to downtown compared to MXP, but either way you need to go to Milan Central train station to catch a train to the Cinque Terre. From LIN to the station the best option is a taxi or bus. From MXP, which is far from the city center, it's is cheaper to use a train or a bus to Milano Centrale.
If your destination is only the Cinque Terre, consider looking for a flight to either Pisa (PSA) or Genoa (GOA). Pisa has a direct non stop from JFK with Delta. It's a seasonal flight that operates 4 days a week from June through August. Pisa is really close to the Cinque Terre.
Genoa has no non stop connection to NYC, but there are flights via other European hubs (such as Paris CDG) to GOA. Genoa is also close to the Cinque Terre.

MXP is the international airport of Milan, LIN is a local airport

Alina

Mary,

If you're flying directly from the U.S. to Milan, you'll most likely be arriving at MXP Terminal 1. If that's your first stop in the E.U., you'll need to clear Passport control, which usually doesn't take long but will depend to some extent on how many flights arrive at the same time and how many officers they have on duty.

Once all the bureaucracy is finished, make your way to the airport rail station and buy your tickets to Milano Centrale via the Malpensa Express (be sure to board the train to Centrale and NOT Cadorna), and also the whichever C.T. town you're going to. Before boarding the Malpensa Express, DON'T forget to validate your ticket!

Which of the five towns is your destination? It would be easier to offer more specific advice if you could provide more information, as the rail travel options from Milano Centrale will vary slightly depending on the destination. You may also need to validate your tickets prior to boarding the train to the C.T., but that will depend on which type of trains you'll be using. You can research the rail travel options using the Trenitalia website. Also, what time does your flight arrive?

Happy travels!