Mixed-market economies have more private property, while command economies have more public property.
Which is the best example of public property in a mixed-market economy?

The best example are roads.
USA economy is a mixed-market economy. It blends elements from market economy with elements from planned economies.
Private ownership is prioritized ( free market economy)  but the government has control over some public services such as healthcare (to an extend), physical infrastructure (the road system), education, national defense, the postal system and some public lands.
The idea behind public ownership of these services is that they are better performed by public than private enterprise.
The roads in the USA and their infrastructure are funded by taxes (especially the gas one), tolls and user fees.