Airport recommendation when leaving Vernazza Cinque Terre to fly back to U. S.

When traveling to CT we flew to Pisa via Frankfurt and it worked really well. Definitely check out Genoa also.

Genoa is closest, followed by Pisa. Milan and Bologna are about twice as far away. Depending on your final destination, a Genoa departure would take you to one of the major European hub airports for your connection to the States. Depending on the flight combination you select, you should easily make a connecting flight on the same day. But it will mean an early morning departure from the CT to tye airport. Or preferably a transfer to a hotel near the airport the evening before.

Pisa. The train connection is the easiest - from Pisa Centrale there's a special short, frequent train directly to the airport called PeopleMover.

And will we most likely need to spend 1 night wherever we are flying out of?

Yes.

Any departure that connect to a US bound flight will be early in AM so being in the departure city the night before is the best plan.

Joe is correct regarding morning times for your itinerary. There used to be early-afternoon flights out of Pisa which could get you home 'same day' (local time, from CET origin), but those schedules were taken out around the time of COVID. In 2015, we flew a 12:50p (United-codeshare) Air Dolomiti [PSA] to MUC; with 1h45m layover for a Lufthansa connection to SFO, arriving back around 7:00p. Best now to plan for an airport-vicinity (Pisa or Genoa) overnight, and wheels' up early.

Which would be the most convenient airport to get to for a flight back to the U.S. (oklahoma)?

The most convenient airport would be the one offering the fewest number of connections on a flight with a final destination of Oklahoma. That could be Milan - a nonstop back to the States might eliminate a connecting flight.

Thank you all for the information! I will start looking at flights and figure it from there.