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Cambridge Online Dictionary and Oxford Dictionary defines the meaning of "Gonna" as
Gonna : Informal for going to.
But,
I'm gonna New York.
sounds odd to my ears.
I personally feel that "gonna" should be followed by a verb and its usage with a noun is wrong but I couldn't find any source to confirm it.
I want to ask if this sentence and my assumption regarding the same are correct or not? And why is it that no source mentions this rule?
You are correct. Gonna is not short or informal for all senses of going to. The only relevant sense is the "modal" sense, where going to indicates the future tense. Going to in the sense of travel or movement does not shorten to gonna.
As for why sources don't mention this, I think the main reason is just that documenting any language is very difficult, and documenting English grammar and vocabulary is monstrously difficult. Dictionaries and especially textbook grammars seldom get the language right. While this particular omission is pretty simple and easy to correct, there is no realistic way to document all of these kinds of oddities. The moral for someone learning English is: don't put too much trust in authorities writing abstractly about English; you should learn mainly by example from real usage.
I have just written, an answer that shows the difference between gonna (the informal way to write and the natural way to say) the semi-modal verb be going to. It is followed by a verb in the bare infinitive form:
I'm going to (gonna) write you a letter.
This is different than the present progressive of the full verb to go, which is never pronounced or written as gonna:
I'm going to New York.
The following is ungrammatical:
*I'm gonna New York.
