are you gone? I do not know ... however, I am Italian and I live near Rome, so I know quite well, if you are gone the information can be useful for others who are planning to make your same trip.
rome for a week is little, if you then want to go to venice, 6 hours drive from Rome, going, visit it one day and came back you lose 3 days and for Rome remain 4 days.
What to see, first of all imperial Rome, the Colosseum, Roman Forum, Palatine, Circus Maximus, the Baths of Caracalla, without forgetting the Appia Antica, everything is pretty close, only the Appia is far away. then one day it may be enough.
then the Catholic Rome, Vatican, but every church, even the smallest have unique works of art.
while turning to the churches in the center the most beautiful thing is to get lost in the small alleys and maybe meet the true Roman life. turn to the typical markets, as campo de fiori, buy a supplì or a calzone in a pizzeria in the center, or to take a real espresso at the tazza d'oro in front of the Pantheon.
other days you could walk to the center in via del corso or in Villa Borghese , go to the Capitol, throw a coin in the Trevi fountain or relax in Piazza Navona or Piazza di Spagna eating an ice cream.
go for a tour of less touristy in Trastevere, beautiful of day, fun at night, or Testaccio, where you can still eat the tail or pajata, Here in the night is full of people.
or go to the Jewish Quarter, where you can eat the artichokes at the giudia.
If you like museums, as well as the Vatican, the Sistine Chapel is attached to these, visit the Capitoline Museums, the Borghese Gallery, the Museum of the Imperial Forums, or for modern art, the macro and gnam.
try not to scrub at the center, from the resturant, from the ice cream maker, if you want good things, look for them a little further away.
if you want to go to venice, beautiful, along the road passing through Florence, which is worth a stop. but before you must cross the south of Tuscany, if you exit the highway at Montepulciano, you'll be in the area of the great Tuscan wines from Chianti and Brunello di Montalcino, Montepulciano to. here you can visit Pienza or Siena. everything in just 2 hours from Rome.
around Rome, only 1 hour of driving there's Perugia with its historical center, l'aquila and the small villages of Abruzzo, or the south of lazio, where I live, non-touristy, but with beautiful historic-gastonomic trails or more down to the recommended peninsula sorrentina with Amalfi, Ravello Sorrento and Positano.
the cinque terre are to the north and out of reach in the itinerary rome venice, but are to be seen. unfortunatly an avalanche has recently made ​​a lot of damage.