Senatus Populus que Romanus
It's hard to talk about Rome and not sound like a cliche. It's marvellous, it's eternal, it's romantic, it's historic, it's fun, it's all that and more. There are so many things to see and do, that it is hard to pick. It helps if you love history and art, but it's not a must. Even if you don't, you will enjoy just walking around, people-watching, eating great food, drinking wonderful wine, and shopping if you are into that. We stayed at the Sheraton Rome Hotel & Conference City. Given how far it is from the center, it only makes sense to stay there if you are using your Sheraton points and staying for free (which was the case for us). If you are paying for hotel, find the one in the center. Sheraton does offer a bus to the city, it is 3 euros per person from the hotel, and free from the city back to hotel, but the bus goes every 1.5 hours, so you have to plan carefully and buy tickets the day before during the busy season.
We recommend you start with Forum Romanum- the remains of the glorious and powerful Roman Empire. To really be able to imagine how it looked at its peak, you can buy one of those books that have pages that overlap pictures from past and present. Do not miss the Colloseum- tickets are app. $13 and you can buy them online. Instead of taking the tour, we downloaded Rick Steve's audio guide which had sufficient information, especially combined with another guide book.
Another not to miss thing in Rome is the Vatican. You should schedule your visit ahead of time and buy the tickets online- you will have to wait in line regardless of the reserved tickets, and should do this visit when you are fresh as there is a lot to see and lots of walking and waiting involved. But it is so worth it. Do not miss the Sistine Chapel and Michelangelo's Creation of Man.
If you have time have coffee at Piazza Navona and enjoy the Fountain of Four Rivers, eat lunch at Campo di Fiori and acknowledge Gordiano Bruno who was burnt there at the stake in the XVI century for his cosmological theories that defied teachings of the church. You can buy some nice shoes when in the neighbourhood. We recommend skipping Fontana Di Trevi- you cannot get a good glimpse anymore because of the crowd of tourists- it's not worth it in these circumstances.
For good and inexpensive food, cross the river and explore Trastevere. It has great restaurants, less tourists and excellent bars. And don't forget to come back.