In Rome, I would plan ahead. Unlike some other cities in Italy, it's not that easy to get around. Mostly because Rome is just big. I would check out what areas you want to visit and arrange to walk from one area you want to see to another. Otherwise you would have to take a cab or bus, or walk a long way through areas in which you weren't interested.
First it depends on what interests you. In particular, do you want to see ruins or modern? Or just a general overview? My thought on the varous ruins was that they were magnificent, but depressing, and I didn't want to be depressed on my vacation. If you think that looking at all the destroyed buildings would be your cup of tea, then I would suggest starting at the Coloseum and then walking through the Forum, and up to the Capitaline Hill behind the Victor Emmanuel Monument. From there, it's a short walk to Piazza Navona for lunch, then past the Pantheon (the best preserved ruin-still in use), and on to the Trevi Fountain (a must see, both during the day and at night), then up Via Del Corso to the Spanish Steps, then stroll down the Via dei Condotti to see how the other half shops (or your half). That's actually a lot of walking, which you may not want to do, but you get the idea. Try to have an area you'd like to see, next to the area that you're in so that you don't have a huge amount of walking in between.
One area that my wife and I wish we had had more time in is Trastevere. It's a lovely area of shops and restaurants.
Are you staying overnight in Rome? If you have a choice of where to stay, I would stay close to whatever it is you want to see most. If it's the Vatican, don't stay near the Forum, as that's too far to walk. Speaking of the Vatican. If you are going to take the time to go there, consider reserving a space on one of the subcrypt tours that takes you within a few yards of where St. Peter was buried. Fascinating. You must reserve at least 20 days in advance. Fax: 06-6988-5518. That may be an old number, so check in a recent guidebook. And if you're up to it, climb the Dome.
There's much more, of course. I will try to find our notes on restaurants and send some ideas on those.