Broadly speaking, free cities can be split into two categories, those built in the developed world and those built in the developing world. The different environment of living in either the developed or developing world shapes the logic of free cities.
The developing world is, generally speaking, poor, poorly governed, and urbanizing. This means that improvements in governance can largely be accomplished by copying successful examples. There is no need to reinvent the wheel, only reproduce it. The urbanizing population means that there is a population which is relatively easy to attract to a new city. In practice this means a free city can thrive in the developing world simply by importing common law.
The developed world is, by and large, wealthy, well governed, and urban. This means that improvements in governance must be genuine innovations, not mere copies. Further, the lack of an urbanizing population means that new residents must be drawn from existing cities. One avenue for free cities in the developed world is to attract technology companies. Google, for example, has said they do not invest in health care because it is overregulated. An environment of permisionless innovation could create a thriving free city in the developed world.