Most people under 40 speak english just fine, over 40 is hit and miss. Public transportation is decent and on time, you have local buses going everywhere. Every bus stop has info printed out with bus's line numbers and where they go to. You can buy tickets at any new stand, most people don't even bother with it however.
Fairly low crime, you won't get mugged or anything like that. Avoid taxis if you can, they are vultures and tend to grossly overcharge foreigners. Gypsy beggars are not uncommon, just ignore them.
If you need accommodations and it's only for a few days like you said, renting an apartment per day is likely cheaper than airbnb and the like. Here is a good website for it with pictures and ratings. It works well and its relatively inexpensive, depending on how many people you got with you.
1200+ Apartments in Belgrade, from budget to luxury, studios to 4 bedroom apartments. Best rates with discounts. Find yours, book now with Stan Na Dan Beograd +381 65 42 43 500
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If you like museums and want to see the military museum, I also recommend checking out the aeronautical museum, they have a quite a collection of war planes. It's located near the airport too.