Geographically, Belgrade is rather like Pittsburg. It was built around a fortress that was built at the meeting point of two rivers - in this case the Danube and the Sava. The fortress now contains Belgrade's grand military museum - most famous for the fact that it contains various captured US military hardware, including parts of a stealth fighter the Serbs shot down, and a US Humvee parked outside.
The most fascinating thing about the military museum is what it doesn't talk about. The museum is quite large and dedicates a lot of space to the first world war and the second world war, but the detail stops in 1945. Although there are exhibits of equipment captured from the Americans, there is no mention of what war this may have been part of. Similarly, there are displays of weapons captured from the "terrorist groups" of Kosovo and the "illegal armed groups" of Croatia, but no context at all. This felt particularly weird given the huge amount of space dedicated to the background for all their other conflicts. More generally I got a feeling throughout the day that the Serbs don't want to talk about their recent wars, except to occasionally remark about how they have "very bad leaders".
Probably the most interesting relic from the war is the bombed out military headquarters, which has been deliberately left in it's post-NATO condition as a memorial - supposedly to the firefighters who died in it. The architecture of Belgrade is very grand - almost reminiscent of London. There are many large ornate buildings, most of them either government buildings or religious buildings. There is also a pleasant pedestrianised downtown area with shops and restaurants.
One thing that surprised me a little was how much the Serbs look like the Bosnians. Given the bitter conflict between the two I had expected there to be some clear distinguishing features, but the two groups look pretty much indistinguishable. Perhaps the Serbs and Bosnians can see a difference, but I couldn't.