I thought we already HAD floating cities.
How large is the crew and supernumeraries on a modern Nimitz class aircraft carrier. It even has its own airport and independent power supply, in the atomic reactor system that powers the ship and desalinates the water supply, and has modern communication systems all up and down the spectrum.
They do have to make a port of call from time to time to replenish perishable and expended supplies, but other than that, they have a very flexible travel schedule, and the wide range of climatic conditions in the world make seeking out the most optimal place to relocate into a much more straightforward task.
Good idea but Aircraft Carriers have those icky weapons of war.