One of my favorite things to do in Rome when it's too hot to keep walking: find a spot in the shade on one of the stone benches in Piazza Navona and sit and watch and listen. Pretty surroundings, a light breeze, and interesting people from all over the world walking around admiring all the same things as you are.
The most beautiful window, always full of flowers. I even saw it in a guide book once- it's famous!
The next night, there were people having a cocktail party up there. At one point, they opened that window, leaned out over the piazza in their tuxes and dresses and began to wave to all of us sitting in the piazza.