Rome/Amalfi coast

The Amalfi Coast is 20-40 miles south of Naples. Naples is approximately 150 miles south of Rome, and there are fast trains to take you there. The trains are the most economical way of travel from city to city in Italy. If you go to the Amalfi Coast, you'd need to have the time to spend touring both Naples and Pompeii. I wouldn't suggest you cutting your trip short in Rome, as it deserves a full week's time to itself. I'm saving Naples and the Amalfi Coast for our next trip to Rome.

Rome is in the middle. Venice is 4 hours north of Rome, by train (or 6 hours north by car). Naples is 1hr 10min south of Rome by train (or over 2 hours by car, depending on traffic).
Amalfi Coast is 1+ hour south of Naples

Is this a day trip from Rome? You can get to Napoli Centrale in about 1hr10min on the fast train. At Napoli Centrale, you go downstairs to take the Circumvesuviana train to Sorrento. It's about the same travel time to Sorrento. Then, if you want to go down the Amalfi coast, you either take the SITA bus or the ferry. All together, you are looking at approx 6 hours to get to the Amalfi coast and back to Rome.

kristie, It would help to know the time frame of your trip? The suggestions I provided in my other reply would be different if adding the Amalfi Coast. As the others have said, it's easy to get there via "regular" train from Rome and then Circumvesuviana to Sorrento, but realistically the entire trip will likely be about four hours. I would not recommend driving in that area, as driving in Italy also has some potentially expensive "caveats". You may find it very helpful to buy a copy of the Italy 2013 Guidebook (available now), as it has all the information you'll need. It's also available as an E-book in several formats, and apparently the 2013 edition has now been converted to E-book also. It would help to have a bit more specific information on your trip. If you add the Amalfi coast, you may have to skip something else. Cheers!