It is rude to say this so please don't. It's here to practice vocabulary and structure.
Are you old?
Are we old?
Study English in London
Good question. It's a question regarding the difference in the preposition.
'in' means within the hotel.
'at' means within and around the grounds of the hotel.
Let's look at two pictures.
Here you are 'in' the walls of the hotel. You can say:
'...stay in the hotel...'
'...stay at the hotel...'.
Both are okay.
Here you are around the hotel (in this picture you're near the swimming pool). You can say:
'...stay at the hotel...'
These are some example conversations:
A: Which hotel are you staying at / in?
B: The Ramada in Ueno. Do you know it?
A: Yes, it's lovely.
Both are okay because you will stay (sleep) within the walls.
A: What do you want to do today?
B: I just want to stay at the hotel.
This means 'in' the room but also around the hotel: swimming pool, restaurant, bar, games room etc. Therefore we must use 'at'.
A: How was the trip?
B: Great but the hotel I stayed at / in wasn't brilliant. It was dirty and not very comfortable.
A: I'm sorry to hear that.
Both 'at' and 'in' are okay here because you are referring to the room and the building.
Hotel Grand - Advert
Welcome to the Hotel Grand. At our hotel you will find an amazing pool, world-class dining and lively bar / club for adults. In each room there's a widescreen television, with Netflix, minibar, hairdryer and all have ensuite facilities.
'At' is used to talk about the facilities.
'In' is used to talk about what's in each room.