Almost all correct!
But remember that when you are giving details about an event in the past, you must use the past tense:
- I didn't go to the same places you visited, I went to New York.
(You have to use past simple here, because it's a statement about a particular trip)
- Oh I haven't been there.
(This is possible as a standalone statement, if you are talking about your life experience in general. However, in the context of this dialogue, it would be more logical for the person to say 'I didn't go there', meaning 'I didn't go there (when I was in the US last year)
I'd like to see it. Did you go there with some friends?
(This has to be in the past simple, because you are referring to the specifics of a trip that took place in the past - not about the person's general life experience. You cannot use a present perfect here).
Otherwise, all good! It's a tricky area of grammar, and you seem to have the right idea. Well done.