That's the first thing I thought...
I mean it's nice that they are trying but wouldn't they all be dead or dying?
I assume the city agency initial communications would sound kinda like * *.
The pinnacle of communication into and out of the directly-affected area would be CB, military-grade hardened tactical radio nets, and field telephones, any of which would have to be provided by responders going in, because none of it would be left in the strike zone. Most of the CBs within a couple of hundred miles would be fried by EMP, but a ground burst does at least minimize the EMP effect and limit its range, even if it does maximize the fallout and neutron-induced radiation.
The cell towers, servers for the fiberoptic, and switching stations for even the older landlines would all be gone, and any sort of network dependent on a NYC node would be down. Even the radio commo would suck (For the radios that didn't have their semiconductors and chips slagged by the EMP) because of ionization from residual radiation.