Ever since we got put up here for the night after missing a connection on Air Serbia back in 2013, it's been our go to hotel in Belgrade. It's super cheap and the express airport bus starts and terminates just across the square. There's also a popular place to get really good šiš čevap sandwiches 24hrs a day (Grill Ranković, opposite McDonald's) just a couple steps away. However, our favourite thing about the Slavija is the old-fashioned Yugoslav charm - it's almost like nothing has changed since the early 1970s, it's truly amazing and like going back in time. The service is also great, and they're very flexible and laid back with late check out and such things. If you fancy nice views, request a room on a higher floor facing St Sava Temple.
Our only complaints are the terrible internet (it's basically non-functioning in the rooms, but it's usually okay for checking email in the lobby - if you're staying in Serbia more than a couple days, just get a mobile internet card and hotspot your phone) and the lack of AC in the summer. If you're someone who prefers modern conveniences over old-fashioned charm, you might want to consider other options, as virtually everything in the economy rooms dates back many decades (except for the towels, which we noticed were new as of mid-2017), and while we love all the character, we can see why others may not be so keen.