After 10 visits to Rome anywhere from 1-7 days we have finally figured out the best way to see the best sights (IMHO) in one day if that is all you have (i.e., cruise boat port, short layover before flight):
1. Start at Forum and pick up your prepaid ticket to the Forum and Colisseum. Walk around the Colisseum and take a quick 30 min peek inside. Make sure you bypass the ticket line after security and go directly to the turnstiles.
2. Cross the street, bear left, and enter the Palantine Hill entrance (shortest lines) to climb Palatine Hill (bear left after the turnstiles). Check out the ruins, and then enter The Forum via the side gate.
3. Walk through The Forum and see all the well-marked ruins. Exit at the Capitol Hill End.
4. Climb up Capitol Hill and bear right to enter the back door of Chiesa Santa Maria Aracoeli - one of the prettiest churches in Rome (see Rick's tip).
5. Exit the front door of the Chiesa Santa Maria Aracoeli and bear right past the glass elevator that goes to the roof of the Vittorio Emannuel monument to the Caffeteria Italia for lunch. Excellent views of the Forum and Rome. No need for the pricey trip to the roof.
6. Walk down the Chiesa Santa Maria Aracoeli steps and walk 20 mins to the Pantheon to see the best-preserved Roman architecture in the world.
7. Take a taxi or other transport to the Vatican Museum where you have a prepaid ticket waiting.
8. Visit Vatican Museum and exit out the back directly to St Peter's (see Rick's tip).
9. Visit St Peter's and call it good or visit an excellent restaurant for dinner like Antica Griglia Toscana, Dal Toscana or ZiGaetana - all a few blocks southeast of St Peter's out of the touristy area.
Hope this helps a few...