I went on vacation to Peru and went sighting to Machu Piqchu.
I went on vacation to Japan and went sighting to Mt. Fuji.
I went on vacation to the country and went sighting to the beach.
No matter if the monuments are famous or not?
If A is a monument, but neither well-known nor a typical travel spots,
can I say "go sightseeing to A" still?
You asked a good question.
"Sightseeing" in English is translated to some phrase which literally means "see the views", and mostly refers to "city tour".
That's the reason why I hesitated using it in somewhere out of a city.
I think I understand it better now.
Thank you for correction.
I will be carefull to not make the same mistake again.
No one would say I went sightseeing to the beach. Going sightseeing and going to the beach are two very different activities. Neither would they normally use the word sightseeing when talking specifically — that is, about a particular visit to a particular place. “We’re going sightseeing” means we’re off to see the sights, in a general sense:
We went sightseeing · We went on a sightseeing trip
We visited Buckingham Palace, the National Gallery and Covent Garden.
We went sightseeing to Buckingham Palace, etc.