The weather in Rome Italy is almost always mild, winters are rarely cold and snow is uncommon. December through February is the coldest period with temperatures averaging around 55F or 13C.
The best time to visit Rome is definitely from late April through to mid June. Temperatures are warm but not stifling and evenings are very pleasant, although in late April and early May you may need a light jacket.
Another good month is September when you'll find the weather to be pleasantly cooler and a lot less humid with plenty of wonderful sunny days. Most times short-sleeves will be fine during the day while a light jacket or sweater will suffice for the evenings. The other good thing about September is that you'll find Rome to be far less crowded with tourists too.
Early October can also be pleasant, although it is a little less predictable from a weather point of view. You can be unlucky even in early October and get day after day of rain but you can also be lucky and get glorious sunny days.
Unfortunately the months when most people visit Rome are the months during which the weather is at its worst. These are the months of July and August, not only is the weather stiflingly hot and humid but the city is overrun with tourists.
August is particularly bad, most Romans have closed up and gone on vacation and any authentic Roman atmosphere has almost entirely disappeared.
Late October and November too are best avoided, this is the period when most of Rome’s rainfall occurs and rainy miserable days are common.