She booked a room at the hotel.

Literal

She [topic-は] that hotel [at-に] room [object-を] reserved.

予約する ('to reserve, book') is the standard verb for restaurants, hotels, train tickets, and appointments. The に here marks the place where the reservation is held — the location-binding に rather than 場所で. Where English says 'book a room *at* the hotel' with the same preposition for both an event location and a stationary place, Japanese reserves で for the place where action happens and に for the place where something exists or is anchored. A hotel reservation is anchored at the hotel, hence に.