Airports to fly in and out of based on destinations Venice, Florence, Cinque Terre

Besides Venice and Florence's airports, obviously, for the Cinque Terre you can look at Genoa and Pisa as possible airports.

You can make a logical, open triangle in any direction and need not close up the third leg - need not return to your origin. Book it as a "multi-city" flight plan, such as into Venice and out from Pisa or Genoa. Milan and Rome have more flights, but these airports probably have enough to work for you. Avoid a very early departure out of Venice which might require an expensive water taxi; timing is usually better in the inbound direction. In other parts of Italy, too, if you don't want a very early departure, you might stay a night at a European connection city like Amsterdam.

Best: fly into Venice, fly out of Pisa or Vice Versa (Genoa can be switched with Pisa if you find flights there better)
I did not consider the Private Water Taxi cost unreasonable for the service provided so personally would not be turned off by an early morning Venice departure. I would opt for the water taxi departure even with a flight at a different time.

Most cost effective might be a R/T out of Milan and is still doable but will mean more time on a train and may require an overnight or more in Milan to make the times work.

Since there are not too many direct flights to Italy from the US you need to weigh all of your options and make the best choice for your dates, departure city, preferences on layovers, etc...

Airport info:
Venice: closest airport is VCE. The VCE airport is the 3rd intercontinental airport in Italy, therefore lots of options. It is in the mainland, while the historical center of Venice is in the middle of the water. Therefore It's great to fly into, but kind of difficult to fly out of if your return flight is in the early morning.
Florence: closest airport is FLR. The FLR airport is a small airport, but very convenient since it's practically downtown (only 15 min away from the historical center). It has numerous connections to CDG (AirFrance), FRA and MUC (Lufthansa), ZRH (Swiss), AMS (KLM), among others.
Cinque Terre: The closest airports (PSA and GOA) are at least 1.5 hours away. Both airports have similar connections to the ones mentioned above for FLR. Since flights to North America depart in the morning, it may not be the best choice to leave the Cinque Terre as your last destination in your itinerary, because you would probably have to spend the night closer to the airport as the Cinque Terre are a distance away. But it would work as a first destination.

Based on the above I would try to have Florence as my last stop, because flying out of Florence airport is very convenient. Flying out of VCE is ok if you can get a flight directly to the US, since those depart later in the morning. VCE has seasonal (summer) direct connections to ATL, JFK (Delta) EWR (United) PHL (American).
FLR, PSA, GOA have no direct flights to North America therefore you need to connect somewhere in Europe for those destinations.