There are two large central parks in Sofia: Borissova Gradina and Yuzhen Park and several smaller ones that you would only really visit if you happen to be staying in the area. The large parks have wooded areas that can almost have you believing you are out in the country and not in a capital city, but the busier parts of them, including the children's playgrounds, are unkempt and noisy. Horseback police patrol Borissova Gradina as do police on bicycles. People make full use of the grass areas for picnicking, playing games and even organised workouts. Watch out for dog muck - most Bulgarians still don't clean up after their pet!
Even if they seem pleasant and safe during the day, avoid wandering around the parks at night as muggings are not unheard of.