Rome Airport...On the Way

To maximize what I'm going to be able to see on this short business trip to London, I chose - can you imagine - to take a longer flight involving a stop-over in Rome. On the way to the conference, I was only in Rome from for 3 hours - enough to change terminals, get a bottle of water, and sit and wait for the next flight. On my way home in a week, I'll have 12 hours - and hope to see something. With the time it takes to go to and from the airport, it's likely that something will be one thing and so I have to decide...what.

If you were in Rome to see one thing - what would it be?