- I have been to London three times.
- I have gone to London three times.
are grammatically correct, ans both seem quite natural to me, although I believe that the version with "been" is significantly more common.
Thos Google Ngram supports that belief, although with the usual cautions about using Ngrams to determine usage frequencies.
Sentences such as:
I am going skiing next week.
are also perfectly proper and natural.
- I have been skiing three times.
- I have gone skiing three times.
are grammatically valid and natural, and may be used whether the events are recent or long ago.
I have skied three times.
is valid and natural whether the events were this afternoon or five years ago. The form
I skied three times.
is more likely to be used of the recent past, but can be used for a specified defined occasion or period, such as:
- I skied three times last fall.
- I skied three times in my teens.
Constructions using both "been" and "gone" can be used to refer to the experiences of others in a similar way.
The construction suggested in another answer:
I have gone skiing for three times
strikes me as odd and unnatural, I would avoid it.