。
She has been living in Otaru the whole time.
Literal
She [topic-は] the-whole-time Otaru [in-で] is-living.
小樽 (Otaru) is a port city on Hokkaido's west coast, famous for its preserved early-20th-century stone warehouses lining a picturesque canal — relics of its boom era as a herring-fishing and trading hub. Today it's a major sightseeing destination known for sushi, glass crafts, and music boxes. The で here marks the place of the lifestyle (暮らす describes the broader life-living rather than just residence), distinguishing it from the residence-marking に that goes with 住む. ずっと gives the durative 'the whole time'.