。
She sat down next to me.
Literal
She [topic-は] my next-to [at-に] sat.
となり (隣) is the immediate-adjacent 'next to' — used for the seat right beside, the house next door, the table immediately adjoining. The に here marks the destination/landing point of 座る ('sit'), pairing with verbs of motion or positioning to indicate where the action terminates. A bare, compact statement of fact: she sat down beside the speaker.