Piazza dell' Anfiteatro - not the center of the city but to some, the heartbeat, is always a great spot to eat, people-watch, or stand in the center and turn slowly in a circle to appreciate the surrounding unbroken oval - old men in hats sometimes do odd things. The low tents are all outdoor restaurants.(Panorama - click to view in full width if your browser supports that action).
A view from atop the perimeter wall looking outward. Large villa-styled buildings mostly line the adjacent street. The mountains in the distance separate Pisa from Lucca.
It's difficult for a tourist to turn a corner without seeing something spectacular. The bell tower of the Church of San Frediano peeks out between buildings on this narrow street.
I went to Villa Bottini to see an art exhibit.
It was quite nice but, I think I may have been more enthralled by the ceilings in some of the rooms of the villa more so than the art exhibit itself.