Hi R.C.
The answer to what restaurant really depends on if you've been before to Belgrade.
K. Terrase restaurant is actually an intermational restaurant that also has good local dishes. It's a place I recommend and go to myself in the summer (or nice weather) because it has a large outside terrace with views and live classical music. Food and service excellent, polished and prices if you choose national food and local wine, a really good meal is probably equivalent of £20 per head. Its still nice to visit in winter, they will have piano or some live music but you won't get to see or use the wonderful terrace so it's less atmospheric. Some food and wine is expensive here, but you can see on the menu and avoid the high prices.
Your hotel is ideal location opposite on Terazia, a main street, on foot you can walk just 50 metres to the pedestrian shopping street, along here to Kalemegden and the restaurant is about 15min walk.
If you want to 'go local', somewhere typical Serbian I would recommend you go to Sport Restauran, especially now as they have an english menu, that's only recent introduction. Note: Sport has no music, no great atmosphere, it's just a nice place - don't judge it from how it looks outside, go in and see!. It's on Autokomanda, you can take a trolley bus from opposite side of the street to your hotel to Slavia, then take No9 tram to Autokomanda 3 stops away from Slavia. Or you can take a taxi, a taxi rank is actually outside Sport Restaurant. You won't find many (or any) tourists here.
Note:
If you've never been to Belgrade before, for national food with music, them go to Skadarlija, just 10 walk from your hotel, the oldest street with old famous national restaurants. This are is probably the one tourist type area in belgrade, but there is some good food and ambience. Once youv'e been there to experience it, then you'll find better food at Sport, overall ambience and polished service at Terrasia.
A possibility is a drink in Skadarlija, then taxi to Sport. It's very hard to know what you would like. Sport is just a basic restaurant, but serving great local food. The other two have more special feeling. Skadarlija is full of history and atmosphere that must been experienced. All these restaurants are a similar price as Terasse - by Belgrade standards expensive but good value in Sterling compared to what you'll get in London for £20.
I hope that's 'food for thought'.
Regarding beer, if you like lager then the local 'Jelen' is very good when on draught. I'm fairly sure your hotel has it! :-) Ask for Jelen on tap, all waiters close by speak english.
Lots of places near to you, out of your hotel and turn right, just 40 metres as the street bends to the right is the Old Tavern pub, good place to start, have a beer and plan yoir evening.
Have fun
Stoofer