Parks seem to be in short supply in Rome.  If you get to Via Vento, continue on past all the shops and cafes until you get to the old Roman wall and go through it an you will find the start of a large park, keep walking through the park and you will find a huge historic house , the Villa Borghese, that houses art exhibits and has beautiful gardens when you can find some solitude and shade.  If you want to tour the art exhibit, you will need to buy tickets several days in advance, the tickets are about 13 Euros.