‘Coming on the Hudson’ first appeared on the live album “Thelonious in Action”. It is a great example of an “Advanced Forms” composition employing an implied Pitch Centre (Link).
“The tonic continued to exist, and, if necessary, the composer could employ it… but in the great majority of cases, he preferred the concept of a tonic in distant perspective.” Vavara Dernova.
For what it’s worth, we can think of this piece as being in the key of ‘F’. Monk never actually resolves to the “tonic”, “preferring to leave it in distant perspective”. The live video of Monk playing the tune is instructive – as with many of these songs he likes to concentrate on variations rather than introducing new material in the improvised section. The improvs are also grounded in stride and 1-7 voicings in the left hand – Monk blending the past with the future.