Rome’s largest park, Villa Doria Pamphili, contains a stunning, mid- 17th century palace surrounded by garden mazes, jogging trails, fabulous fountains, a superb grotto, and pine lined views of Rome from atop the Janiculum hill. Note that there are not maps inside the park. Your best bet is to run the perimeter paths, which add up to ~10k. There are bathrooms and water fountains near the park entrances.
Great Additional Option to/from the park: From Ponte Sisto/Piazza de San Giovanni, take Via Garibaldi, passing through the Trastevere neighborhood and by important landmarks such as the Piazza de Santa Maria, Basilica di Santa Maria, the floodlit Fontana dell’Acqua Paola, and the Garibaldi statue. Mix it up by going through the Passeggiata del Gianicolo monument with the cannon that goes off at noon, or the switchback road, Passeggiata del Gianicolo. This makes for a ~2.5 mile loop, to and from the park. Hilly.