Travel from cinque terre to united states

Probably train to Milan, Genoa or Pisa, then flight back to the US. Which way to go probably depends more on your flight arrangements than on which Italian airport is the very quickest to reach from the Cinque Terre.

What airport do you want to return to? I use Washington-Dulles, and Milan is typically a lot cheaper than any other Italian airport except Rome. If you prefer BWI or Philadelphia, it may be different for you. So I'd start by checking flights from the three cities I listed; you can throw Florence into the mix as well. Perhaps one of the cities will prove to be substantially cheaper or offer much better connections, which will make the decision easy.

Which airline are you flying?

The Cinque Terre are located half way between Pisa airport and Genoa airport (about 90+ min from either via train). Both airports have only intra Europe flights, therefore no direct flights to the US are available from either.

Since you are near Washington Dulles (IAD), your best bet is with United, which has a hub at IAD. United is a partner of Lufthansa, and Lufthansa flies to Pisa and Genoa from Munich airport (MUC). United flies to MUC from your home airport IAD.

Therefore the best flight would be a United/Lufthansa code share flight from Washington Dulles to Pisa (PSA) or to Genoa (GOA) via Munich, Germany (MUC).

For the return trip to the US you would do the exact reverse.

Lufthansa also flies to Florence (from both Munich and Frankfurt), to Milan Malpensa (MXP). Florence and Milan are farther away from Cinque Terre than Pisa or Genoa.

Lufthansa flies pretty much anywhere in Italy from its two hubs (FRA, MUC). Therefore you could go to Italy anywhere then return from Pisa or Genoa (Via MUC).

Regardless which combination you choose, you almost certainly need to spend your last night closer to the airport of departure because flights to the US depart in the morning and the Cinque Terre are too far from any airport to make an early morning flight.

Frank, there are ferries, but only in calm waters. The waves may be too big in open ocean.

I'm just up the road from you in Gettysburg. I would see who flies from Milan to Philly (no idea if there are any). The drive from Dulles is technically shorter but the traffic is brutal. Took us almost 4 hours last time- should have been no more than 1.5.

Frank, there are ferries, but only in calm waters. The waves may be
too big in open ocean.

The ferries don't figure into the sort of travel the OP wants to do. Trains are the only form of transport that make sense to the closest international airports. The CT towns are also not on an ocean, although rough waters can cancel the ferries; they're on the Ligurian Sea.

But Frank, I would not recommend being in the CT the night before your flight. Wherever it is that you will depart from, you'll want to be close that airport.