It’s been kind of useless honestly. The city allowed the registrars to reserve many domains as “premium” domains, i.e. almost all neighborhoods were reserved with prices in the tens of thousands of dollars. Initially you had to specify a NYC postal address, no PO boxes, allegedly to prevent domains from being scooped up by non-NYC entities. And there was no privacy protection (that seems to have changed).
GoDaddy is the registry, but not the sole registrar that it can be registered through. Both NameCheap and Gandi are options - and I am sure others too.
NB: I work for GoDaddy, but am not responding in any capacity on their behalf.
