。
She's staying at a small hotel near the castle.
Literal
She [topic-は] castle [possessive-の] side [possessive-の] small hotel [at-に] is-staying.
城の側 (しろのそば, 'beside the castle') locates the hotel spatially. 泊まる (とまる, 'to stay overnight') with ~ている indicates an ongoing lodging situation. ホテル is the standard English loanword for Western-style hotels, distinct from 旅館 (りょかん, traditional Japanese inns).