You'll be fine, from all I heard Belgrade is similar to Bucharest, slightly less petty crime, but worse traffic (and traffic related accidents) would sum it up. We don't hate Romanians, people will either be positive about it, or indifferent.
It's been a long time since I've seen people on heroin anywhere in Serbia tbh, most junkies nowadays are on speed, mdma, and ecstasy, and those are usually people going to clubs. The everyday risks are pickpocketing in public transport and busy streets (you know this, you know who does it because they are forced to do it for their alcoholic parents), and getting hit by a car.
Use the daytime to walk around and do the sightseeing, because it's simply more pleasant (warmer, easier to actually see things, more things are open, etc). Go to see the Kalemegdan area, St. Sava temple, St. Marko church, the general city center, Skadarlija, and various museums. As far as food goes, look for traditional taverns, and you will probably be satisfied. Don't fall for the fancy modernist stuff they overcharge their food, and it's usually worse than old school places. Evenings are cool for binge drinking and partying.
Avoid using taxis (they tend to overcharge tourists), busses will be fine enough, and most areas of interest are easily reached on foot.