It is hard to experiment with a Universal Basic Income because of its inherently universal nature.
One argument for UBI is that it replaces existing welfare systems such as unemployment benefits and state pensions. The implementation of existing welfare systems is often on a national level. The benefit of reduced bureaucracy is lost when implemented on a smaller level.
UBI is hard to combine with freedom of movement. It is typically limited to citizens, which is an inherently national concept. There may not be the bureaucracy in place to replace one system by another only for "citizens" of a particular city.
UBI may require the government to raise more taxes than it currently does. Taxes are often decided nationally. Whether taxes are raised based on income, capital, or production, any of those are more likely to move between cities than between countries.
Another argument is that the government may stimulate consumption by enriching the poor; the argument is that the poor are more likely to spend extra money entering their bank accounts. However, this Keynesian effect of economic stimulation only works on a large scale; within smaller economic units, economic stimulation may not work because money can more easily flow out of the system.
None of those objections are insurmountable, but they are all practical hurdles that might limit the ability of local governments to experiment with UBI.