The correct sentence should read "Most visitors who go to New Zealand plan to return someday."
The word "who" is used when referring to the subject of the sentence. In the case of your question sentence, the subject of the sentence is "visitors", with the verb "go."
"Whom" is used when referring to the object of the sentence. If your sentence read, "I enjoyed talking to the travelers, three of whom had been to New Zealand," for example, "travelers" is the object in the sentence.
An easy test to help determine the correct term: if you would substitute "he/she/they" for the questionable word, the correct term would be "who." If you would replace the questionable word with "him/her/them," the proper word would be "whom."