The third thing to do in Rome for free is certainly to visit the Aventine hill, where the Orange Garden and the Buco della Serratura are located. Two truly unique places!
The first is a park with wonderful bitter orange trees and a spectacular view of all of Rome. The garden, whose name comes from the many bitter orange trees growing there, extends over the area of an ancient fortress built near the basilica of Santa Sabina by the Savelli family between 1285 and 1287, which, in turn, was built over an old castle constructed by the Crescentii in the tenth century. The garden is bordered by a wall that once surrounded the Savelli castle and other remains of the castle can also be still seen.
The second tourist attraction is the exciting view of the Dome of St. Peter's Basilica, seen from a unique perspective: the keyhole of the Priory gate of the Knights of Malta.
Staying on the subject of Parks in Rome, it is also worth visiting Villa Borghese and Villa Pamphili, two truly wonderful green lungs of the city.