We walked from Piazza del Populo down to the Spanish Steps and then another 10-15 minutes to the Trevi Fountain so we could throw in our coins. Leaving there, we walked down to the taxi stand (you can't flag a cab down in Rome) at Piazza Venezia and rode down to the "shortest" line to buy tickets for the Forum. (It's south of the Colosseum a ways and goes into the Palantine first.) It's a relatively short ride, but worth the 6 euros for us.
Even with the advertized shortest line, we still stood in line about 45 minutes to buy the tickets. We walked through the Palantine and the Forum with my guidebook. There's something quite amazing about walking on streets where ancient Romans once strolled. It's also interesting to me that fresh flowers still adorn the burial spot of Julius Caesar's ashes. Needless to say, the walk was miserably hot and shade was rare.
We left the Forum and walked the short distance to another taxi stand and rode over to the Pantheon area for lunch. (another 6 euros) On the way, we passed a very loud demonstration near a bank (guess Italians don't like bankers right now.) It was a nice lunch with a great view of the Pantheon (one of my favorite places in Rome). After lunch, I grabbed a gelato and ate it before we got in a taxi for the ride back to the meeting point at Piazza del Populo. When we got in, the taxi driver asked if we wanted the air conditioning on. Without thinking, we said "yes". The taxi ride was 20 euros. I was in shock -- should have asked what it would have been without the air conditioning. Probably about half of what we paid. The funny thing is that the taxi never really got cooled down!
We got there about 45 minutes early, so had a cold drink (iced coffee for mom and diet coke for me) in a small outdoor cafe in the shade. Everyone was on time, so we boarded the bus at 3:45 and got back to the ship at 5:30. Like the day before, the shower felt terrific! Mom and I went to the Ocean Plaza and listened to music, watched people dance, and had a drink before dinner. The dining room was less crowded than usual. Guess everyone was zonked from the hot, but enjoyable day in Rome.
Those who haven't visited Rome should probably do an organized tour to maximize their day in the city. Like many Mediterranean ports of call, Rome requires many days rather than many hours to see everything. Cruise ships like the Carnival Breeze offer full-day tours of Rome and/or Vatican City. Those who have seen the city before might want to visit one spot more in depth, like we did the Forum. The Carnival Breeze also offered tours to Lake Bracciano and through the Italian countryside for those who chose not to go into the city.
The Carnival Breeze docked at Salerno, Italy the next morning.
Carnival Breeze Mediterranean Cruise Itinerary

