Chic, shabby grunge with mid to high end restaurants and bars - Beton Hala (Concrete Hall) - the place to be and be seen. Beton Hala sits on the banks of the Sava River at 2-4 Karadjordjeva Street, in the general vicinity of Savamala. The juxtoposition of high end trendy restaurants and their derelict and dilapidated neighbours is one of the things that characterises modern Belgrade to me. There are some elaborate plans on the books to demolish and redevelop the area, however given it was supposed to be completed in 2008, I think the Belgrade Travel Bug Suite Hotel will be okay for a number of years to come.
Sitting at any of the eclectic restaurants on an evening in summer watching the sun set over New Belgrade, Great War Island and fishermen dipping a line into the Sava river is time well spent. The area is busy though and bookings are recommended if you want an outside table at any of the restaurants. Whilst its fabulous in summer, don't avoid it in winter as the softening of the setting sun against the fog is also a sight to see - especially with a warming glass of good cheer in your hands or some fine food on your plate.
There are plenty of interesting caches in Belgrade which are well maintained by the dedicated and friendly caching community here - check them out whilst you're in the Serbian capital. I guarantee they'll take you places you would miss otherwise.