We are going to stay in/at a hotel .
We are going to stay at a hotel.
When we're talking about what hotel you stayed or are staying at, I understand the preposition of choice is "at" rather than "in."
1. Use "stay in" with large areas such as big cities, towns, countries or continents or streets, areas, zones; means of transport: plane, car, bus, train, ship...
2. Use "stay at" with relatively smaller places: flats, houses, hotels, restaurants, clubs, banks, theaters, cinemas, airports..; some points (điểm): at the corner, at the bus stop, at the door, at the entrance, at the end of the road, at the crossroads, at the front desk...
We are going to stay in a hotel.