In his memoirs Nikita Khrushchev says the main reason he sought to go to Disneyland during his visit was by behest of his wife. He was originally not planning of travelling there, however he made it expressed that he did want to visit, however the American security advisers basically denied it over fear of security. He was upset because he wanted to see the "happiest place on Earth" in person, and as you said, it was ingrained in Western culture as the ultimate place as a destination. He also saw the security concerns more a way to deny him, a Soviet man, from enjoying what was an American thing.

The problem is during the entire visit Khrushchev was constantly followed and "protected" by the Americans. For example during his tour of an Iowan farm, the road was lined with national guard personal from the airport at Des Moines to the farm outside of the city. Each had guns, however for fear that one of them would act a hero, they were not given ammunition. Once arriving at the farm, Khrushchev sought to get out of the eyes of the American media and the American politicians by going out into the cornfield with the farmer, Roswell Garst.

Therefore, honestly he probably just wanted to enjoy a day in America without the prescence of the American media and American security breathing down his neck, however due to his standing as a leader of a foreign country he was not allowed the pleasure.

This isn't a full answer, but I found a speech of Khrushchev's here.

Here is a quote about Disneyland:

"... when I was on my way here, an itinerary was drawn up for me and a program of what I could see here and what places I could visit It was planned, among other things, that I would visit Disneyland. But I have just been told that I cannot go to Disneyland (Laughter.) Why not? I asked Is it by any chance because you now have rocket- launching pads there? (Laughter.) "No," they tell me, "you can't go there because" just listen to this! "The American authorities can- not guarantee your safety if you go there,"

What is it? Has cholera or plague broken out there that I might catch? (Laughter.) Or has Disneyland been seized by bandits who might destroy me? But your policemen are such strong men, they could lift a bull by the horns. Surely they could deal effectively with bandits! Then I said I should like to go to Disneyland just the same and see how Americans spend their leisure. (Applause.) "Do as you like," they answered me, "but in that case we cannot guarantee your safety." What was I to do go and commit suicide? (Laughter.) This is the situation I, your guest, find myself in! It is more than I can understand. I won't know how to explain it to my people. Come to our country if you like, we will go with anyone, you may walk in our streets and parks, and I guarantee that a foreign guest will hear nothing from Soviet people but words of respect and welcome. What am I to say to the organizers of my U.S. tour? I thought you had a well-organized household. Putting me in a closed car and stewing me in the sun is not the right way to guarantee my safety. I thought I could walk freely in your country and meet Americans. But I am told if s impossible. This development causes me bitter regret and I cannot but express my disappointment."

So, largely, I think its because Disneyland represented the epitome of American leisure destinations, and old Nikita just wanted to understand how Americans lived so that he could better understand America.