The apartment is very close to the city center, yet in a quiet area of Belgrade. The Danube river is also close, and you can easily experience different faces of this city (I suggest renting a bike and riding it along the river).
Lower Dorcol neighborhood is one of the oldest in this ancient city. Within the walking distance are also Kalemegdan Fortress and the Belgrade Zoo. It is a safe neighborhood full of shops, bakeries, playgrounds, bus stops, etc. The supermarket is around the corner.