"Went to" vs "have been to"

What is the difference between saying,

I have been to New York and LA;

I went to New York and LA?

I know one is simple past and the other is not. I am looking for how they are used from a native speakers perspective.

The difference is not in the action, but in where your focus is: on the present state or the past action.

I have been to New York and LA.

focuses on your present state: as a person that has visited New York and LA at some time or times in your life.

I went to New York and LA.

focuses on the past action: the occasion of your visit(s) to New York and LA.

"I have been to" indicates that you were there, on a visit, at some point in the past (one or more visits), presumably before any events being discussed in the present conversation. In general, using the perfect construction suggests that the event occurred before what is now being discussed.

"I went to" is more generic in meaning, and hence more context-dependent. Its meaning is in the context of a particular time-frame. So unless you explicitly say otherwise, it suggests that the visit coincided with or immediately followed time period under discussion.

Example where the meanings are distinct

If you had previously in the conversation said that you went on vacation:

• You could say "I went to New York and LA." to tell the listener where you went on this trip.
• It would be odd to say "I have been to New York and LA."; you would be adding a seemingly unrelated piece of information, what you did in the more distant past.

If you are specifying a particular point in time:

• "I went to New York and LA last week." makes sense, whereas
• "I have been to New York and LA last week." doesn't.

Summary

• "have been to" = indefinite, previous time
• "went to" = some particular time (inferrable from context)

"Have been to" is a more personal way of saying "I went to". "I went to" suggests simply something that has happened previously and is being stated is simply a fact. "I have been to" suggests that the completed action has a relevance to the context in which the statement is made that is personal in some way.