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When you think about it, dropping a large heavy object into water will generate a wave but its effect is local and it dissipates rather quickly given a large enough body of water.

It seems to me you are comparing apples to oranges. Your body is not generating a wave extending down to the ocean floor. It is only creating a surface wave. The debris from a massive landslide will reach the ocean floor and therefore generate a tsunami that extends down to the ocean floor as does an earthquake generated tsunami. Some energy will be lost reducing the initial height from 300 feet down to 165 feet but there isn't enough friction between La Palma and the U.S. to dissipate the tsunami.

Of course a mountain falling into the ocean will displace a lot of water and make a darn big splash and cause massive damage to any nearby islands and local shipping, but I’m a little skeptical that NYC would be inundated by a 165’ wall of water.

There is one factor you're not considering with respect to NYC. Long Island Sound narrows as you move towards NYC. The narrowing of Long Island Sound along with the rising ocean floor may very well push the wave height of a tsunami to at least 165 feet and possibly higher.

EVALUATION OF TSUNAMI FAR-FIELD EFFECTS FROM POSTULATED COLLAPSES OF STRATOVOLCANOES

Dr. George Pararas-Carayannis - Paper published in Science of Tsunami Hazards, Vol 20, No.5, pages 251-277, 2002.

…Thus, these models forecast incorrectly tsunami far field effects. Shallow water effects, which are due to the nonlinear nature of the tsunami, are treated as linear and overestimated. Only waves of much longer wavelength can propagate effectively across ocean basins. Even though local destructive tsunami waves can result from the postulated mechanisms, waves of such short periods will rapidly decay away from the source region with considerable height attenuation….

Subsequent modeling by Mader (2001) confirms this and provides realistic estimates of tsunami far-field effects for the same hypothetical La Palma slide. Using the wave profile output obtained from a high speed (110 meters/second), pneumatic landslide generator of the Swiss Federal Institute of Technology at Zurich, Switzerland (Fritz, 2001), and based on a "worst case" scenario for La Palma (650 meter high, 20 kilometer radius water wave after 30 kilometers of travel), Mader's numerical model treats the resulting tsunami as an intermediate wave of short wavelength and period - taking into account both dispersion and geometric spreading effects. Specifically, the shorter period and wave amplitudes in his model, result in significant wave height attenuation with distance - to less than one-third of the shallow water amplitudes. The upper limit of his modeling study shows that the east coast of the U.S. and the Caribbean would receive waves less than 3 meters high. The European and African coasts would have waves less than 10 meters high. However, full Navier-Stokes modeling of the same La Palma failure, brings the maximum expected tsunami wave amplitude off the U.S. east coast to about one meter.