We got a drink at a place called Hush Hush, where a talented guitar-and-accordion duo played evergreen ‘50s and ‘60s music from Eastern Europe. Down the row, at Cantina de Frieda, a cover band was doing a rousing rendition of the 1985 classic “Ja Sam Lazlijiva” from Croatian synth-pop band Denis & Denis. I couldn’t get it out of my head for days, despite knowing none of the lyrics or what they meant.

The cobblestoned Skadarlija district — often compared with Paris’s Montmartre, and where your hotel will likely suggest that you have dinner — is filled with traditional taverns, called kafanas, where bands of five to six musicians move from table to table singing folk songs and taking requests. (We ate at Tri Sesira, which had two accordion-led acoustic bands playing simultaneously.) In the winter, when people crowd indoors, it’s quite common to dance on your table to show your appreciation, should the music so move you.

Even the magnificent Hotel Moskva, a city landmark built in 1908 and where I stayed, had a piano player at breakfast, which really added to the atmosphere of gilded chandeliers and red velvet furniture.

The scene I liked most, though, was in the historical district, Zemun, a former municipality along the Danube that the city absorbed in the 1930s.

There, Iva introduced me to Jasmina Vekic, owner of the 138-year-old fish restaurant, Saran, one of the oldest in the city. Like many Serbians, she’d left in the ’90s and built a life as a businesswoman in Prague. After Yugoslavia dissolved, about 15 years ago, the government sold off a lot of the businesses it owned, including restaurants, and Ms. Vekic had been able to buy this one at a bargain price. She’s now one of the few female restaurant owners in the city. Serbians, she said, shouting over the band in her restaurant, put music above everything. “Even if you’re an 80-year-old Serb,” she said, “you want to have a birthday party and to dance.”

‘The ’80s were the happiest time’

Another night, Iva took me to the concert of possibly the greatest cover band I have ever witnessed, The Gift, at a venue called Bitef Art Cafe Summer Stage in the Kalamegdan Fortress, an actual fortress used to defend against Ottoman invaders that is the city’s most popular public park.

The singer, Jovan Matic (known as Joca Ajkula, or Joca the Shark), wore eyeliner and oozed sexual energy, particularly once he had shed his shirt. They exclusively played New Wave songs from the ’80s (Depeche Mode’s “Just Can’t Get Enough,” R.E.M.’s “The One I Love”). The crowd of mostly twentysomethings knew every lyric.