I tend to agree with DMark that one week is not sufficient for Italy. I’ve visited Venice, Florence, and Rome over a two-week period, and still felt rushed. I’ve also seen those cities on a more luxurious basis–one week for each city–and I know I still have far to see all of these cities in great depth.
However, you can probably get a decent overview of two of these cities within a week. For distance and time reasons, I’d suggest sticking with Rome and Florence (Venice is mind-boggingly beautiful, and I recently posted my recommendations for that city–but I would suggest saving it for a future trip, along with trips to other northern cities like Verona and Padua).
Rome offers so many wonderful sights–you can’t find any better collection of Baroque monuments or Roman ruins. In addition to the obvious sights (the Vatican, the Colosseum, etc.), where else can you see Michelangelo’s Moses (the tomb for Pope Julius II, in San Pietro in Vincoli), Caravaggio’s cycle of St. Matthew paintings (in San Luigi dei Francesci), or the best collection of Bernini sculptures (the Galleria Borghese, which also features wonderful Renaissance paintings, and is set in a picture-perfect park on the northern side of the city)?
The one drawback about Rome is the traffic–the modern city is difficult to get away from (and, indeed, a large motorway bisects the Roman Forum from the Imperial Forums). However, there are several areas that are closed off to the traffic–including such beautiful squares as the Piazza Navona and the Campo dei Fiori–and only Rome has such places as the Pantheon (my all-time favorite building in the world!) and the Spanish Steps (not too far from the gardens that enclose the Galleria Borghese). To get away from the tourist crowds too, you may want to check out the Trastevere area on the west side of the Tiber–which features several good local restaurants (i.e., non-touristy) as well as beautiful Early Christian churches).
I must also speak up in defense of Florence, my favorite city in the world. If you like Italian Renaissance art at all, you’ll be in love–it is a city of museums, ranging from the famous Uffizi to the Accademia (the latter contains Michelangelo’s David). It’s also worthwhile to visit the Bargello, the best collection of Renaissance sculptures in the world (including Donatello and Verrocchio’s own versions of David, plus some early Michelangelos). I would also second (or third) the Museo del Duomo, which houses many of the works formerly in the Cathedral of Florence, including Ghiberti’s Doors of Paradise (the panels that you see on the actual Baptistery–a wonderful, wonderful building in its own right–are actually replicas; the original panels are in this museum).
The Cathedral (or Duomo) of Florence is, in my opinion, one of the most beautiful buildings in the world (for me, it is second only after the Pantheon in Rome). But don’t forget to see the Palazzo Pitti, which houses the Palatine Gallery (almost as comprehensive as the Uffizi). If you like Fra Angelico at all, you would like the San Marco monastery. I’d also recommend several of Florence’s churches, especially Santa Maria Novella (just outside the train station) and Santa Croce, both of which contain beautiful fourteenth and fifteenth-century frescoes.
And speaking of frescoes, if you like early Renaissance painting, you’ll have to visit the Brancacci Chapel to see Masaccio’s frescoes–some of the earliest works of truly Renaissance art.
This site, which is produced by the city government of Florence, contains a plethora of information for Florence visitors–including a guide to public toilets and restaurants (my suggestion for the former is to use McDonald’s bathrooms, which are always quite clean; for the latter, by all means avoid McDonald’s, and search out some of the local restaurants–the ones on the south side of the Arno are nice, as are the ones around the piazza of San Pier Maggiore a few blocks north of Santa Croce).
To round things off, don’t forget to climb up the hill to San Miniato al Monte to take in a fantastic view of Florence and the Arno (as well as to see a quite lovely Romanesque church). Fiesole, on the hill to the north of Florence, is also very nice for views of the countryside, and a nice village in its own right.