。
She decided to stay with us for a while.
Literal
She [topic-は] for-a-while [interval-の間] us [genitive-の] place [at-に] stay [thing-of-こと] [at-に] decided.
しばらくの間 ('for a while, for a stretch of time') makes the duration explicit by combining the adverb しばらく ('for a while') with の間 ('during, in the interval of'). Together they form a slightly more explicit and writerly time expression than bare しばらく. 滞在する ('to stay, lodge') is the formal verb for temporary residence — distinct from 泊まる ('overnight stay') in covering longer durations. ところ functions as 'place' but figuratively as 'home' in this context — 'our place,' meaning where the speaker's group lives. Note: 私達 written with the kanji 達 (rather than the more common hiragana 私たち) lends a slightly more formal feel.