One of the options is to go to the Boyana church (a UNESCO World Heritige monument). After that continue to the Boyana waterfall (in the Vitosha mountain), which is a real waterfall usually during spring.
You can also go to the Golden bridges (Zlatnite mostove - Златните мостове). You have to take the shuttle nr.10 from the Russian monument (Ruski pametnik) for 1,5 BGN. It will take you to the Golden Bridges and from there you can make small hikes.
If you don't want to go out of the city, you can still try going out in some of the parks in Sofia (Borisova gradina, Yujen park, Zapaden park, Lovna gora etc.). They occupy a large portion of the city, but are not well known even by the locals. about 6 years ago