I am in Rome.
Villa Pamphili has been a second home so i am likely biased. It is approx 180 hectares in the middle of the city and it is amazing. There's trails and grass. Wooded areas and open spaces. For me, the fact that it is totally closed to traffic and the amount of non-urban views makes it even better than Central Park. It is best at lunchtime and early morning.
The Tiber run is interesting and relatively new. There are different types of undesirables in the area but relatively manageable. Not my favorite but a good break.
Villa Borghese has way too much asphalt but it is in the epicenter of Rome. There's also Villa Ada which is gorgeous and less known to visitors. Not to mention that you can always go to Ostia with the subway and run on the beach or in a pine park (unfortunately the latter also patronized by hookers...)
Overall the downtown air quality has improved over the years but still could get better.
Leave an email or a phone number if you want a guided tour (depending what pace you want to cruise) while in the suprisingly-green eternal city.
For early morning runs i would suggest Sunday. During the week the roads get congested quite early.
There are two main tartan tracks which are just bustling with runners at lunchtime: Caracalla (close to Colosseum) and Paolo Rosi stadium. But there's also the Farnesina and Marmi stadium track which are quite nice. The Marmi track is particularly gorgeous with the huge marble statues of athletes towering above it. And if you are looking for a major hill to climb, they are both at the foot of Monte Mario which offers and unparalleled and non-trafficky slope (unlike Gianicolo hill) to attack...