Monasteries and convents often have gardens, art work, and even small museums. Visiting one of Rome's monasteries can be a peaceful contrast to the top tourist sights.
Near San Giovanni in Laterano, Rome's cathedral, is Santa Croce in Gerusalemme Church and Monastery complex where the monks tend a medieval monastic garden in the shadows of a former Roman theater, the Castrense Amphitheater, now part of the Aurelian Wall.
On the Janiculum Hill, Sant' Onofrio Cloister has beautiful frescoes and a small garden. The monastery is the final resting place of Renaissance Poet Torquato Tasso and there's a small museum dedicated to him.
If you're interested in seeing more peaceful places off the tourist track in Rome, see David Downie's book, Quiet Corners of Rome (read review).
Sant' Onofrio Cloister photo by Lisa Finerty