。
She lives right near the school.
Literal
She [topic-は] school [attributive-の] right vicinity [at-に] is-living.
すぐ ('right, immediately, soon') paired with 近く ('vicinity') intensifies proximity to 'right next to / extremely close to.' すぐ is one of those small-but-versatile adverbs that means different things depending on what it modifies: with verbs of action it means 'immediately' (すぐ来る 'come right away'), with location words it means 'right' as in 'right next to' (すぐ近く 'right close,' すぐ隣 'right next door'), and as a stand-alone adverb it just means 'soon.' 住んでいる locks the residence into ongoing state — Japanese consistently uses ~ている for verbs of dwelling, marriage, knowing, and other states that English often expresses with simple present.