。
She sat down quietly in the seat next to his.
Literal
She [topic-は] his [genitive-の] next [genitive-の] seat [at-に] softly sat.
そっと is a 擬態語 capturing soft, careful, or quiet motion — 'gently, softly, without disturbing.' Pairing it with 座る ('sit') paints the act of sitting down without making a sound or being noticed. The location of sitting takes に (a destination/landing spot) — ~の隣の席に. 隣 ('next to, adjacent') chains naturally with の to describe spatial relations: 彼の隣 = 'his side, next to him'; 彼の隣の席 = 'the seat next to him.'