I'll soon be taking my first ever flight on Alitalia and took advantage of a long layover (versus a short one) in Rome.

I've never been to Rome and want to see a little bit of the city during the layover. Therefore, I would appreciate some advice from members of the Alitalia sub-forum.

What are the logistics in getting to and from the airport as fast as possible to maximize time in the city center?

Also, is there a place to leave one's bag (I travel with a 22" roll aboard and a backpack) at FCO? Worst case, I could check the bag in N.Y. but that's against my religion.