With prevailing west to east winds Long Island would be inundated with radioactivity.
While most folks there would survive the immediate blast they would get serious radiation poisoning at best.
The entire island would become a “no go” zone for hundreds of years.
Your can stand at ground zero for the Trinity test in New Mexico, which was a surface burst. You also can stand in Hiroshima or Nagasaki ground zeros. With the right approvals you can go to the Nevada test site home to over 800 detonations many of them surface bursts and walk around the craters. Radioactivity falls off fast from fission products most have half life’s in the hours to days range only a few have weeks , months or years. For a surface burst of a one megaton fission fusion fission three stage weapon the initial fallout plume area will be well over 5000 rem per hour a lethal dose in a few minutes. Three feet of wet dirt or several tens of feet of concrete will give protection factors in the 10000 range making it survivable in a properly built shelter underground even if in the direct fall out plume zone. Being in the bottom deck of a multistory concrete parking shelter or basement would also give similar protection factors. Remember the blast zone is not the fall out zone. The fall out zone starts 10 miles or so down wind and stretches for hundreds of miles building will be left standing in those down wind zones outside the blast radius which for a 1 mt is only 4 miles or so. NYC subways would be nearly useless as shelters they are cut and cover types effectively trenches under the streets with steel and asphalt over the trench not nearly thick enough to stop.gamma rays. The deeper parts of Penn station would be a good spot to hide you would have 30+ feet of concrete and steel and dirt over you. Some of the deeper cross station tunnels would offer shelter 38th st station goes under some buildings. Two weeks is the length of time for a 5000 rem per hour field to drop to 1 rem or less per hour at that level you can then walk out of the fallout area to safety. Even a full days walk is then 24 rem a survivable dose 500 rem is the lethal dose and people have lived with 250.