She stayed at the hotel for several days.

Literal

She [topic-は] several-days that hotel [at-に] stayed.

滞在する (たいざいする) means 'to stay (at a place for a period)' — more formal than 泊まる (to stay overnight). 数日間 marks the duration: 'for several days.' ホテル is a loanword from English 'hotel.'