You are not near the center, you are in the city center. Pedestrian zone Knez Mihajlova and Republic square are five minutes far from apartment. Apartment is in front of the historical site, the Parliament. Belgrade fortress Kalemegdan is only far in fifteen minutes of walk through Knez Mihajlova.
Nearby you can visit a number of restaurants, with domestic and international kitchen, pubs, cafes, grocery shops, pharmacy, exchange office, fast food, bakeries.