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.
Even if the parks seem pleasant and safe during the day, avoid wandering around the parks at night as incidents of muggings have been known to happen. Borissova Gradina has horseback patrol and some other parks have private security surveillance. The big open area outside NDK is well lit at night and fairly safe.