Get on a bus on Via Salaria and visit Villa Ada, which is slightly more local than, say, Villa Borghese and very beautiful. There are plenty of lawns, where you can rest in the shade of trees or sunbath if that is what you want. (Just remember that it is a no-go to get naked in Rome's parks. This also includes sunbathing with a bra or bikini, which is only meant for the beach).
In the park young Romans meet for a football game, they play bongo drums, and the children enjoy life. During the summer months the park offers plenty of evening entertainment in the form of world music concerts and lots of different ethnic restaurants. It is the Municipality of Rome, which since 1994 has organized the event called Roma incontra il mondo (Rome meets the world). A great initiative, that is worth experiencing, if you are in Rome during summer.
Via Salaria 275. www.villaada.org
Villa Sciarra and Villa Doria Pamphili
At the other end of town, at the Gianicolo hill, you find Villa Sciarra and Villa Doria Pamphili. Villa Sciarra is compared to the Villa Doria Pamphili microscopic, but it is incredibly beautiful, and it has a magnificent view over Rome. Villa Doria Pamphili is both the name of the park and the incredibly beautiful white villa which lies inside the park.
Villa Pamphili is the biggest park in Rome, and there is literally room for everything. There are areas in the park that are almost transformed into outdoor sports areas, and everywhere you can see Romans running, cycling, doing gymnastics or even tai chi. Families go for a picnic, old couples take a walk, and of course all of Rome's dogs are being walked in the park. An amazing and very beautiful place.
Villa Sciarra: Viale Adolfo Leduc. Villa Doria Pamphili: Via di San Pancrazio.
Last but not least the Parioli district has a little hidden treasure. At the end of a small side road, overlooking the city and St Peters, is the beautiful park of Villa Balestra, which even many Romans do not know. Here is a basketball court and an amazing playground, lots of green areas and last but not least a wonderful outdoor cafe, which during summertime, stays open until midnight, so you can enjoy the fresh air for a cocktail even in the evening.
Via Bartolomeo Ammannati.