While it is possible to walk or take public transportation between some of these locations, for the sake of time, it may be best to hire a private driver for the day. This will cost around $200-$300, but it will give you the flexibility to see everything on this itinerary without worrying about missed trains or navigating unfamiliar streets.
If you have more time, consider visiting additional sites in each city. For example, in Paris, you could visit Notre Dame or the Palace of Versailles. In Barcelona, you might want to check out Park Guell or the Gothic Quarter. In Rome, the Vatican and the Pantheon are both worth a visit. If you have less time, consider skipping the Eiffel Tower or Sagrada Familia, as these sites can take a while to explore.
Europe has many international airports, so your itinerary will depend on where you are flying in from. Some of the major airports include Charles de Gaulle Airport (CDG) in Paris, Barcelona El Prat Airport (BCN) in Barcelona, and Leonardo da Vinci-Fiumicino Airport (FCO) in Rome. All of these airports have public transportation options to get you to the city center, but you may want to consider hiring a private transfer if you have a lot of luggage or are arriving late at night.