First we need to examine the dragon. It is a fast, armored, ground-based weapon capable of firing a projectile, and operates with a high degree of intelligence and autonomy. Does this sound familiar? To me it sounds like a Tank. Perhaps a bit hungrier and wigglier than the traditional models, but a Tank nonetheless.
With that out of the way, let's talk about how to engage it. As a few people have been discussing, the dragon is tough, but not invincible. Typical small arms fire is going to be useless, but .50 BMG seems to be at the lower edge of effectiveness, so we'll start there and work our way up.
There are also four conditions to consider alongside the effectiveness of the weaponry:
Minimizing civilians casualties and property damage
Stopping the dragon as soon as possible, death of dragon not required but not forbidden by any means
Obeying the chain of command (Proper procedure for calling SWAT, national guard, etc.)
Preventing mass panic
These restrictions limit exactly which weapons and tactics we can employ against the dragon. There are, of course, aircraft which would obliterate the dragon with little effort, and even ground-based weaponry that will suffice, but most of those options are culled by either consideration 1 or, surprisingly, consideration 3. Obviously we could just nuke the dragon, or carpet bomb it, or use any number of very, very destructive munitions, but you don't want civilian casualties or property damage so we can't do any of those things. Also, since this is a domestic emergency in New York, we are limited to the weaponry deployable by the NYPD SWAT teams, the New York Army National Guard, and the New York Air National Guard. Luckily, I think I have found some suitable weaponry accessible by each of the three branches.
The SWAT teams are going to be the first to respond to the "disturbance". Small arms obviously aren't going to work, and men on the ground are going to get roflstomped by the dragon, but as soon as they notice it has no wings it won't take long for them to deploy in Helicopters. A couple aircraft with sharpshooters armed with .50 BMG weaponry might even be enough to put the dragon down all on their own, no National Guard involvement needed. You mention a vanilla .50 BMG will hurt the beast, but not penetrate its hide. Luckily for our intrepid SWAT team, the .50 BMG AP (Armor Piercing) or "Black Tip" cartridge is far scarier (I know from experience it can penetrate at least an inch of steel). There are also .50 BMG API (Armor-Piercing Incendiary) and .50 BMG HEAPI (High-Explosive Armor-Piercing Incendiary) rounds that can do even more damage, though they are probably harder to acquire.
The next step up on the escalation would be the New York Air National Guard scrambling from Hancock Field Air National Guard Base in Syracuse. To my surprise, the NY Air National Guard has only a single combat wing of aircraft and they are all MQ-9 Reaper drones. At first I was a bit disappointed, but I think this is a blessing in disguise. Reapers are unmanned, so we won't lose any pilots, and they're smaller, slower, and arguably nimbler than traditional military fixed-wing aircraft which means they are better suited for engagements in an urban environment, plus they can still carry a wide variety of weaponry. They might not be A-10 Thunderbolts, but they can carry Hellfire Missiles, which are specifically meant for use against armored targets. If the .50 BMG toting SWAT sharpshooters couldn't bring down the beastie, the Reaper Drones armed with Hellfire Missiles will probably do the trick.
Finally we have the New York Army National Guard (I can't say which specific regiment, since it seems the NY Army National Guard gets deployed overseas on a semi-regular basis). From a tactical perspective, if the Army National Guard is involved, then the SWAT teams have failed and the Air National Guard will be having a go. Unless the Army National Guard has any FGM-148 Javelins (and I have found no evidence they do) then the ground troops will likely be little more than fodder for the dragon. The National Guard is, however, quite good at handling emergencies in general. Civilians will be panicking since that's what civilians do best during an emergency, and panicking people do not make good decisions (like stfu and gtfo, for example). If the Army National Guard isn't helping in the fight then they can be managing people, getting them away from the dragon as the Reaper Drones go to work, and handling the general evacuation of the area alongside the police and other emergency workers. It might not be glamorous, but I feel that in the spirit of your question, this job is probably the most important of them all.
So that's how I see things going down. Hope it helps.