Belgrade's old town, Stari Grad, which sits south of the Danube and east of the Sava, is the place to start your walk, specifically the pedestrianised avenue Knez Mihailova. Its handsome 19th-century buildings are filled with shops and cafes, and in the evening it becomes the favourite place for the Balkan version of the passeggiata. It's also home to the Beograd Art Hotel, the first boutique hotel to open in the city.
Stroll north-west past the shops and souvenir kiosks. At the end of the street is Kalemegdan - Belgrade's fortress, historical heart and green lungs rolled into one.
There's also a zoo, restaurants, museums, towers and gates from the Ottoman and Austro-Hungarian periods, and plenty of footpaths through landscaped gardens. It's easy to spend half a day here just ambling about, but head straight towards the giant plinth overlooking the Sava. You can't miss this unmistakable monument, nor Ivan Mestrovic's statue of a victorious warrior on top. From here you can see the route you'll take on the other side of the Sava and the Danube towards the suburb of Zemun.
Take the path directly in front of the statue to leave the park and turn right. Immediately, you'll see a busy junction where you turn left into Kneza Sime Markovica. In the first street on your left you'll notice a restaurant simply called '?'. Built in 1823, it's the oldest tavern in Belgrade and one of the few Ottoman-style buildings remaining in the city. If you're in need of a pick-me-up, ask for a kuvana kafa, a Turkish coffee. That'll get you buzzing.
Carry on until you reach Brankova street and turn right towards the Sava river. Cross the bridge and go down a stone staircase on your right. Now take Usce's shaded riverside path and see Kalemegdan's venerable fortress in all its glory.
You'll also walk past the first of nearly 200 floating bars and restaurants, which come in all sizes and architectural styles. Some are playful in their architecture, such as Monza, which has plonked a racing track on its roof. Others, Blaywatch (website in Serbian) for example, are playful with their spelling.
After about 25 minutes the path curves left and meets the Danube (Dunav in Serbian). Within a few metres is the entrance to an army base, so take the next turn on the right, Kej Oslobodjenja, to carry on past more splavovi along the quayside.
As you get closer to Zemun, the atmosphere takes on a seaside-resort feel, with a mini funfair, children's playground, the Grand Casino and ice cream sellers on the left, and the Danube poking between the splavovi and the trees on your right.
If you're ready for lunch at this point, try the fresh seafood at Zabar. It's pricey for Belgrade (with fish mains starting at about 1900 dinar/(NZ$24.55), but dishes such as grilled octopus and river perch are beautifully done.
As Zemun's old town comes into view, you might start to wonder if you've stumbled into Hungary by mistake.
Zemun was part of the Austro-Hungarian empire until 1918, and it's here that you notice the architectural differences between east and west - Austrian-style church spires, cottages in deep shades of ochre and terracotta.
Zemun is the most attractive of Belgrade's suburbs, with the added allure of riverside restaurant terraces and, further along the quay, pontoons for swimming. Every summer, the authorities lay a pontoon bridge between Zemun and Veliko Ratno Ostrvo, or Great War Island, in the Danube, where there's a small beach in the corner of what is almost entirely a nature reserve.
At this point you can turn left into the pedestrianised Gospodska street, site of the daily morning food market, towards the main thoroughfare of Glavna. From here catch the 84 or 706 bus (pay 120 dinars directly to the driver) back to Stari Grad.
The club scene in Belgrade changes with bewildering rapidity, and even well-established spots can disappear or mutate into something new.
The legendary Underground near Kalemegdan is the newest casualty; late last year it was turned into Soho Republic, a touch of London's Shoreditch in the middle of Belgrade.
Ada Ciganlija, an island in the Sava river, above, is Belgrade's summertime playground, with beaches, watersports, cycle hire and numerous cafes and activities.
- INDEPENDENT