So, when do we use present perfect and not past simple or continuous? Well, to simplify it a lot, we use present perfect to talk about experiences until now, to say you have this experience or you don't have this experience.
"I", the verb is "visit" or "go" to "New York". Remember, we said present perfect is for experiences, so, we use that grammar.
"Have" and the v3. Now, when we want to say "go to a place to visit it", we use the verb "be", the v3 of be.
Why? Just because English. The sentence "I have been to New York", this means I have this experience.
If I want to say I don't have this experience: "I haven't been to New York". But if I say to you "I have been to New York", you just know that I have that experience: "In my life, I have been to New York."
You don't know when exactly, why, with who, you don't know any details, nothing specific. If you want to talk about specific details of that experience, then you use past simple or past continuous.
For example, "Have you been to New York?" Do you have this experience or not? "Yes, I've been there." Yes, I have this experience. Now, specific details about that experience.
That is when we use past simple or continuous. "When did you go?" That's past simple.
We're asking specific details about that experience in the past. And of course, the answer "I went last year."
That's a past simple answer, not a present perfect answer. You would not say "I've been last year."
