What's the best way OUT of Cinque Terra?

Which airline are you flying?
SFO is my home airport too. I go to Italy at least once a year (Florence is my destination usually). SFO is a major United hub (I also have lots of UA miles), so my preferred route is with a UA partner with the Star Alliance (UA, Lufthansa, Swiss, SAS, Turkish, etc.). All of the aforementioned airlines have non stop flights from SFO to their respective hubs in Europe (Frankfurt, Munich, Zurich, Copenhagen, Istanbul).
The airports closest to Vernazza are Genoa and Pisa (each about 90 min away by train). Both have Lufthansa flights to Munich. Then from Munich you can catch the Lufthansa flight to SFO (United codeshare). I think Genoa also has a non stop to Frankfurt (still Lufthansa). From FRA there are 3 flights daily to SFO.(operated by either Lufthansa or United in codeshare).
Another option is AirFrance (part of the Skyteam alliance with Delta). Both Genoa and Pisa have AirFrance flights to Paris CDG (operated by Hop! an AirFrance affiliate). Then from CDG you can connect to SFO with 2 non stops daily (both operated by AirFrance with Delta codeshare). Pisa also has a Delta non stop to JFK in summer. From JFK you could then connect to SFO still with Delta.
Via Amsterdam is also an option, with Transavia/KLM. However there are fewer flights from Pisa or Genoa to AMS.
The largest airports in Italy are however Rome (FCO) and Milan (MXP). You might have more choices of airlines and cheaper prices from those two. They are a bit farther however. The Cinque Terre are about 4.5 hours from either.

Milan. There is a direct train connection from Monte Rosso. That train does not stop in other Cinque Terra towns.

pamela,

Genova, Pisa and Florence are all smaller airports and therefore not as likely to offer direct flights on international service. From Vernazza it's a fairly easy trip to either Milan or Rome, so you might check the flight options there (although you may have to spend one night in either city prior to your flight home).

Roberto will probably be able to tell you which of those cities offers the best flight options.

Milan would be my choice as well.

I fly out of Pisa on Lufthansa with a change in Germany. The advantage is a departure time just after noon so I don't need to stay over as I would have to do leaving from Milan.

I fly out of Pisa (Alitalia/Delta) connecting in Rome.

We took the train back to Rome from the Cinque Terra.