Time to go home

Most flights would be from Rome, Milan then Venice

There aren’t any direct flights from Florence or Bologna

I believe Bologna is shortest train trip

Definitely choose a flight directly back to the US, not one with a plane change in Paris, London, Amsterdam, or other city outside of Italy.

Being "Captain Obvious", Rome and Milan will have the most choices and Florence and Bologna are the shortest train ride from Urbino.

Kind of boils down to where you want to spend the night before you fly. How much the cost of the various option may affect your choice is something only you know.

Can you not just do the reverse of how you got to Urbino?

EDIT- Misread where 'home' is so deleted the irrelevant parts of my post

American also flies FCO to JFK direct.

But is this a one-way flight? How are you getting to Italy in the first place?

If it is really one-way, I suggest you look at Emirates. They fly direct from Milan MXP to JFK. The price in Economy Flex in April is 407 euros. AA charges $2357 for FCO to either JFK of ORD on the same date.

Where are you flying to?
United has direct flights from FCO to IAD and EWR

A one way is going to cost

Thanks to all of you
for helping. It is convoluted for us to get home from Europe: we are in Durango, CO, so we would probably get a flight to Denver from Italy. We are initially flying into Naples to see friends in Praiano, on the Amalfi coast, then working our way by train through Spello and Urbino.

It will be less expensive if you book your round trip now
Do a multi city search
In to Naples
Out of Rome or Milan

There won’t be any direct flights either way but purchasing the entire trip on one ticket will save you a lot of money
Purchase from the actual airline NOT a reseller like Expedia, kayak, etc

Go to skyscanner.com. You can search flights from your home airport to IT.

There are no direct flights from Italy to DEN.
DEN is a United hub therefore your best bet is a United flight or a flight with a Star Alliance partner, such as Lufthansa, although AirFrance also has a direct flight from Paris CDG to DEN.
The easiest option is probably to take the train to Bologna the day before your flight, then take a Lufthansa/United codeshare flight from Bologna to Denver with one stop either in Frankfurt or Munich.

Alternatively you could go to either Rome or Milan (Italy’s first and second largest airport respectively).
From either there are plenty of options, including the aforementioned Lufthansa flights via Frankfurt or Munich. If you want to stick with United, United also has non stop flights from Rome FCO to Newark, Chicago, and Washington Dulles. From Milan MXP United has non stop flights to Newark and Chicago.

No matter what option you choose to Denver, there will be at least one layover, either in Europe (Frankfurt, Munich, or Paris if flying with AirFrance) or in the US (several options from Rome or Milan).

If you are looking to fly directly from Italy to the US, Rome or Milan are the only options. However the closest decent size international airport to Urbino is Bologna (but only European flights, with Lufthansa being the major carrier serving that city).