She stayed at the hotel.

Literal

She [topic-は] hotel [at-に] stayed.

The basic 'stay/lodge' frame: 泊まる takes に for the lodging place, plain past 泊まった for a completed event. The verb 泊まる is specifically for overnight stays at lodging — distinct from 滞在する (a longer stay, often translated 'sojourn') and from 住む ('to live, reside permanently'). Japanese carves up 'stay' across these three verbs by duration and intent, where English needs adverbs to disambiguate.