Denver to 2 days in Barcelona or other city and on to Rome, if possible

I am not sure what you are trying to accomplish. The flight times from Denver to any of the European hub cities is going to be within one or two hours difference. Is there a max to the number of hours on a plane? About the only way to shorten the flight time would be to fly from the east coast maybe New York, Boston, Washington DC. We don't have many direct flights from Denver so you most likely will be changing planes in the US. For example - Den to Amsterdam is about 11 hours, Rome is 13 hours and London 9 hrs all with a change in the US. NY to London is about 7 hours. The direct flight to Frankfurt is close to 10 hours. And getting to Barcelona is difficult from Denver for a total of about 17 hours. Icelandic air is doing some promotions you might look at their schedule.

As to comfort and service they are about the same regardless of the airline. All pretty miserable in economy. Economy Plus/Comfort available on some airlines is an improvement but I don't know if that would be enough for you. Obviously if you need comfort then it is business class.

A more complete explanation of your needs, might help us to give you a better answer.

If you would like to stop on your way to Rome from Denver you could easily fly from Denver to a major hub in Europe. There are flights from Denver direct to London or Paris for example. You could get off in either of those cities for a couple of days and then take an inexpensive European airline to Rome. That flight will only be a couple of hours. I was also able to find a few direct flights to Rome from Denver. I would consider British Airlines. They flight from Denver to London or Paris and even Rome. They are a nice airline. My experience has been that the European airlines usually have better customer service and are more comfortable than US carriers. Iceland Air tends to be the least comfortable.

We've used British Airways for most of our flights to Europe, and the Denver to Heathrow direct flight is much more comfortable than Americal Airlines flights we've taken. They've cut back on some coach passenger comforts over the years (no more complimentary sleep masks), but are better than some. The farther back you sit in coach, the less likely you'll be listening to crying babies. Business or First Class will give you more comfort, for a price. Lufthansa from Denver to Frankfurt has also been not-completely-miserable. London's not the cheapest place to lay over for a couple of days, but is One of the Great Places in the World. You will have to get yourself from Heathrow Airport into the city, and then back to Heathrow to continue your journey, which could almost break some people's banks. With BA, it sometimes involves a 2-to-5 hour wait in the terminal for your connecting flight, but you can connect to Paris, Madrid, Brussels, and even Barcelona. So flying from Denver to Barcelona, with one change in London, is definitely possible. If the train interests you, take the Eurostar from London to Paris, then when you're ready to continue to Rome, you could fly, or stick with the train. France's high-speed TGV train will get you part of the way. It sounds like maybe all your arrangements for Rome are complete, but for coming home, the Hilton at Rome's Fiumicino Airport is adjacent to the terminal, really convenient for connecting with an early-morning flight, has a stupendous breakfast buffet, and afforts a good night's rest before flying Rome-London-Denver.