The best time to visit Rome is in October to April when most of the tourist crowds have dissipated and room rates are slashed. Weather this time of year hardly ever gets below freezing. For summery weather- without a bunch of tourist and the intense humidity- come in May or September. Rome receives a Mediterranean climate that features hot, dry summers and rainy winters.
What is there to do?
When in Rome you are able to go to the Colosseum. The site of many a bloody gladiatorial fights the Colosseum, which was finished in 80 A.D., could then hold about 50,000 spectators. Today, the massive complex is a favorite site amongst travelers. That said, you'll find lengthy lines almost anytime you visit. To beat the queues, you can purchase a ticket at the Roman Forum, which allows you admittance to both the Colosseum and a line jump.
Roman Forum while not as popular as the Colosseum (but located nearby), some say the Roman Forum is more interesting (and free!). Although much of the complex is in ruins, you can see the remains and imagine the former glory of the Roman Empire.