The biggest effect on tourism in New York is the infrastructure damage that will be long term. Long Island was inundated. I live in the second highest area of New York, and the damage here will be in the millions from fallen trees alone. There is also the short term issue of supplying the boroughs with staple products as many roads are impassable and bridges still closed. Breezy Point ruined. We live miles away and could smell the smoke of devastation late into the night.
My friend's house was utterly destroyed. Will insurance companies will default on the sheer number of flood claims? New York City's major attractions: Broadway, Museums along Fifth Avenue, and mid-town are on relatively high ground, so a lot of tourism destinations in terms of Manhattan geography are not affected. Air travel will recover relatively fast. Mass Transit will not recover as fast because of salt water tunnel flooding, which was a worst case scenario. But tourism tends, again, to be focused on Manhattan's mid-town, not the other boroughs. Thus, the 2, and 3 and 4 and 5 trains are viable, at the very least.
Bridges and tunnels will open relatively fast.