Arrive Fiumicino (FCO) and take a pre-booked taxi or Leonardo Express train to city center; settle into a centrally located 3-star/4-star hotel near Termini or Centro Storico.
Enjoy classic Roman pasta (carbonara or cacio e pepe) at a nearby trattoria such as Trattoria Vecchia Roma or Da Baffetto; good way to taste local ingredients.
Drop bags at Florence hotel (near Duomo) and take a walk to see the cathedral and Baptistry; Duomo visit typically open 10:00–17:00 (climb dome requires ticket).
Short flight back to Athens (~45–50 min). Arrive and check in to a hotel near the airport if you prefer early departure next day, or in the city centre.