Buckminster Fuller had this idea many years ago, but instead of helium, he had an insight into geodesic domes that suggested when built large enough, they would become hot air balloons.
Calling it a "Cloud Nine", Fuller's thinking was
A half mile (0.8 kilometer) diameter geodesic sphere would weigh only one-thousandth of the weight of the air inside of it. If the internal air were heated by either solar energy or even just the average human activity inside, it would only take a 1 degree shift in Fahrenheit over the external temperature to make the sphere float. Since the internal air would get denser when it cooled, Bucky imagined using polyethylene curtains to slow the rate that air entered the sphere.
So the heat of the sun warming the air, the waste heat of internal machinery, the heat that human beings always throw off through activities and so on will generate enough heat for the "Cloud Nine" to remain suspended in the air.
Geodesic sphere. A Cloud Nine will be built like this
The real issue isn't so much if such a thing could be made, but how it would sustain itself? Economically, it is totally dependent on supplies being brought to it from the ground. What it could "produce" might be things like software and entertainment (scripts, videos, music etc.), but it is difficult to imagine a self sustaining economy based on that.
Politically there are also issues about overflight (the people on the ground might not think much of a free flying city passing overhead. Who does it belong to, who do the inhabitants pay taxes to and what business do they have hovering or flying over your territory in your airspace?).
Given these obstacles, flying cities might best be tethered over areas with spectacular views, and generally be recreation and tourism complexes.