is this sentence wrong? why? should I only use "which" instead of "where"? why?

It is wrong because your friend did not recommend "where"; your friend recommended the hotel, and that is a "which". (Furthermore, "of ours" is completely unnecessary.)

You would use "where" if your friend had recommended a location: "We stated at the Plaza in New York City, where a friend recommended we stay."

Technically, "where" could be taken to mean at the specific location within the hotel rather than the hotel itself. That may be why your friend suggested "which" is preferable.

You can't recommend "where." You recommend a *place*. So, speaking of the hotel: "which a friend recommended."

that was recommended.

Yes

but a hotel is a place

...... which was recommended by our friend.

We stayed at the Park Hotel, that a friend of ours recommended. Is the word you're looking for i'm pretty sure! :-)

Where is used for place. .In this context a hotel is not a place so which is correct.

"Where" is not correct as written. Use "which" or "that."