If I people ever asked me about Rome all I could said it is a very hectic city and ancient in it's own way. One thing for sure the traffic is really mad here. Red lights could means go and vise versa. So just watch out where you're going in Rome. :->
Nevertheless, it's an awesome city to explore! You could get around Rome by walking if you have the will - (in the city center I mean). Well it's almost the only way to discover any other places in Europe is by walking around, get lost and find your way back. ;-) There's underground system that will cost 4 Euros for unlimited ride in a day (it includes the bus as well). :P
And if you're in hurry you could make every other important tourists attraction all in a day.
Amongst places that you must go if you ever come to Rome are
* a) The Colloseum
b) Roman Forum ruins
c) The Pantheon
d) Piazza Navona
e) Piazza Spagna
f) Piazza del Popolo
g) Basilica @ Vatican City
And if you had more days to spend in Rome of course you could go and discover even more :->