We arrived around 9am and had the chance to walk around the Piazza while it was still relatively quiet. I know on cannot complain about tourists crowding a place as I was one of them. So please do not misunderstand. One gets a nice view of several of the historic sites from this square and it was lovely to sit on one of the benches and have a picnic lunch. There are also lots of restaurants, should you wish to brave the crowds. We found the gladiator and Cleopatra look-alikes in front of the Arena very entertaining as they tried to get tourists to take photo's with them, after which they charge a fee for being part of your photo. Their facial expressions, depending on whether the particular tourist paid/ignored/cheated them were quite entertaining during our picnic.
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