One of my favorite places to relax over the day was Piazzale Caffarelli on the Capitoline hill, just right and the end of the stairs before you enter the Piazza Campidoglio.
There were some benches under old big trees with the perfect view direction north, quiet and high above the street (v.d. Teatro Marcello). Last time I was there, it was closed because of construction works.
Has anyone an idea whether it is re-opened?