When using the present perfect "has/have gone", the implication is that he has not returned and is still in Europe. With simple past tense, there is no such indication: he may still be in Europe or he might have returned.
Incidentally, you would normally use "Mirek went to Europe on business." when the time of the action is understood between both speakers, so the context might indicate whether he is in Europe or back where he came from.
Both are acceptable grammatically.
In the first, the object clause is written in the imperfect tense (past continuous). In the second it is written in the past tense.
Neither example can possibly imply that the person described as 'you' is still staying at the hotel. But the first could well imply that 'you' were still staying at the hotel at the time 'I went'. But with the 'when you were in New York' clause included, it does not seem possible that I could have gone to the hotel when you were still there.
Edit 4 July 2020. When I wrote this answer nearly six years ago I said "it does not seem possible that I could have gone to the hotel when you were still there". I think that was a mistake. I don't now believe I meant that. It seems perfectly plain that option 1 leaves open the possibility that my visit to the hotel took place while the other person was still there.
It does not matter that the principal verb in the sentence (went) is in the past. The action of 'I went' has nothing whatever to do with the tense applicable in the object clause. One could equally well say:
'I went to the hotel where you will be staying when you are in New York', or 'I will go to the hotel where you were staying...'
I think both sentences mean almost exactly the same thing. The second is perhaps more applicable to a very short stay, where there were also stays at other hotels.
The French would always use the imperfect (imparfait) for this type of thing, but in English you have the choice.
Best Answer
Speaking as a native British speaker, I instinctively see the difference as follows.
When going to school I wore necklaces with starfish pendants. ---> When travelling to school I wore necklaces with starfish pendants.
When I went to school I wore necklaces with starfish pendants. ---> When I was a schoolchild I wore necklaces with starfish pendants.
My explanation is that they are two different idioms. Notice however that in English, the context for the sentence could make a difference to the meaning.
Note: I can't speak for US English. I imagine it is the same.