I have been to Rome four times and like Frank Sinatra now I do it my way. The first time was with a church tour. It was a whirlwind three days of seeing many things but not able to spend time really looking at things. The second time was with my friend, her son, my daughter and me. We rented an apartment for a week just across the river from the Vatican. We got to see almost everything we wanted to see. The next two times were on cruises and I took the excursion "Rome on your own". The bus dropped me off in front of the Vatican and I was free to explore on my own.
Roman Catholic church dedicated to "St. Mary and the Martyrs" but informally known as "Santa Maria Rotonda." The square in front of the Pantheon is called Piazza della Rotonda. For more information on the history of the Pantheon go tohttp://en.wikipedia.org/wiki/Pantheon,_Rome . One of the amazing things with this building is that there is a hole in the roof and there is an area cordoned off if it rains because the floor is wet.
Doing Rome on my own I spent several hours in St. Peters and actually attended Mass that morning. Then I walked from there to Piazza Navona and from there the Pantheon. I had lunch in a little restaurant called Antonios. My favorite restaurant in Rome. It's on a side street off the Partheon. Papa Antonio welcomed me with a glass of white wine as I sat down. Lunch was gourmet. From there I walked over to the Trevi fountain and tossed some coins in the fountain to insure I will return to Rome. It was a wonderful afternoon doing my thing in Rome. I walked back to the Vatican in time to catch the bus back to the ship.
I've been to Rome in March, May,and twice in December. I recommend going in early December. The weather is possible rain with temperatures in the 50's but there are no crowds at the attractions. March was cloudy and rainy but uncrowded. May was hot and crowed. The Trevi Fountain looked like an ant hill and St. Peters was wall to wall people.