In the first option, it is not right to use both a comma and "and" to connect a two-element list of modifiers ("vibrant" and "very diverse"). In the second option, a comma should not be isolating the adverb "very" from the adjective it modifies (diverse). Only the third option is properly punctuated.
The correct answer is "New York is a vibrant, very diverse city".
Explanation:
The last option is the only sentence correctly punctuated. The first sentence is wrong because it is not correct to divide two phrases by a comma and the conjunction "and", it is only correct if it is one or the other possibility. And, the second sentence is also wrong because it is not necessary to have two commas in the sentence just before and after the word "very".
