Buckminster Fuller speculated on this as far back as 1960 with his "Cloud 9" Tensegrity sphere. The basic idea is to continually increase the size of a geodesic sphere until the mass of the air trapped within is greater than the mass of the structure (Fuller calculated that a sphere with a radius of 1320 feet would rise if the internal temperature were 1 degree f above the ambient temperature, essentially the largest hot air balloon ever. Obviously this is the "minimum" case, so would be unable to lift very much outside of the supporting structure.
However, increasing the size of the sphere increases the volume, so more lift will be delivered. Some calculations of the effect can be found here: Can Cloud Nine be built?
Scale models of megastructures. The Cloud 9 floating on the upper left may be the size of some proposed arcologies, but only houses about 7000 people
Cloud 9 to scale with existing skyscrapers
The real issue isn't "can this be built", although even with 1960 era technology it would be somewhat questionable, but rather the economics and logistics of operating the thing.
Given that even the largest conceivable Cloud 9's on Earth would have a limited lifting capability, virtually everything will need to be imported, and the city will require some sort of high value product or service to export in order to convince people to sell them food, manufactured products and so on. Since the Cloud 9 is extremely massive but also quite delicate (much like an eggshell), high value products or services will be at risk all the time from threats of invasion to bad weather events.
So while it is "possible" to build a Cloud 9, you really need to dig into the worldbuilding to understand "why" this was built and "how" it is sustainable over a prolonged period of time. I don't know of anyone actually trying to work out the economics or logistics of supporting a flying city like a Cloud 9, and I suspect there would be a multitude of other issues, such as the immense shadow, airspace rights and even how or if it should be tethered to the ground.
I would also have to question the idea of traders willing to pay tax to dock at an intermediate port. As a Zeppelin captain flying cargo, it seems much cheaper to fly directly to and from the cities and avoid paying surcharges to load and unload cargo at a Cloud 9. After all, how do they plan to stop me? Unless there is a very clear advantage to using the Cloud 9 as a "port", which you would have to identify, it seems like a monumental "prestige" structure which would consume a lot of resources to build, but never really pay back on the huge investment.
So yes, if someone is willing to pay the price and the technology allows it, a geodesic sphere over a kilometre in diameter would indeed function as the basis of a flying city, and can remain in the air so long as the internal temperature is higher than the ambient air temperature outside the sphere - which might be possible through solar energy and waste heat of the people and equipment inside. On the other hand, paying for and sustaining such a structure is not going to be easy, and you will need to identify the clear and compelling reasons that people will go through all that effort.