Drones: Most “No Drone Flying Zone” signs are meaningless

Only the FAA regulates airspace and many “No Drone Flying” signs are not legally enforceable.

The myth of the ‘No Drone Zone’ sign: What you should do if you see one: Digital Photography Review (dpreview.com)

Factfulness

Here is what the FAA has to say about this:

FAA Statement–Federal vs. Local Drone Authority | Federal Aviation Administration

State and local governments are not permitted to regulate any type of aircraft operations, such as flight paths or altitudes, or the navigable airspace.

However, these powers are not the same as regulation of aircraft landing sites, which involves local control of land and zoning. Laws traditionally related to state and local police power – including land use, zoning, privacy, and law enforcement operations – generally are not subject to federal regulation. 

Cities and municipalities are not permitted to have their own rules or regulations governing the operation of aircraft.

However, as indicated, they may generally determine the location of aircraft landing sites through their land use powers.