The city destroyed by Ultron in Avengers: Age of Ultron is Novi Grad. It is the capital of Sokovia, the fictional Eastern European country associated with Wanda and Pietro Maximoff.
During the film’s climax, Ultron lifts Novi Grad into the sky using a massive machine beneath the city. His plan is to drop it back to Earth like a meteor, creating an extinction-level catastrophe that would imitate a natural disaster and eliminate humanity.
The Avengers evacuate civilians while fighting Ultron’s army across the airborne city. Thor, Iron Man, Captain America, Black Widow, Hawkeye, Hulk, and the newly allied Maximoffs work to stop the plan. Quicksilver dies while protecting civilians, and the city is ultimately destroyed after the Avengers prevent it from striking Earth.
Sokovia is the country; Novi Grad is its capital city. Sokovia is therefore a tempting but technically incorrect answer. Seoul and Johannesburg are also locations featured in the film, but neither is the city Ultron raises and destroys.