She lived in the suburbs of Tokyo when she was young.
Literal
She [topic-は] young days Tokyo [of-の] suburbs [in-に] was-living.
東京の郊外 (the suburbs of Tokyo) uses 郊外 (こうがい, suburbs/outskirts). 住んでいました uses the polite past progressive — she was living there during that period. The polite ました gives this a conversational, storytelling quality — someone sharing biographical details about a third person.