I think you are right. This is about the size of the Hiroshima/Nagasaki weapons, and note that they were *air bursts*, about 500m above the ground IIRC, for max blast effect. The effects of a ground burst would be less.
Seven million people commute into Manhattan each day. Almost two million live on the island. Few of the residents commute out of the city to work. This means that on the average work day there are at least 8mm people on an island that is 13 miles long and 8 miles wide at its widest point. A groundburst anywhere in midtown would almost certainly kill a million people.
The effects would be somewhat contained by the concrete jungle itself, but look at the economic and psychological impact from the loss of just two buildings in 2001. It could be hundreds of buildings even with a small nuke, and the loss of life and economic trauma would be devastating.
Unfortunately the fallout from a ground level blast would be orders of magnitude worse then with an air burst. Lots more interesting radionucleides to deal with afterwards too.