My father goes to his office in Shinjuku every other day.
Literal
Father [topic-は] one-day interval [at-に] Shinjuku [in-に] exists his office [to-に] goes [polite-ます].
一日おきに means 'every other day' — おきに expresses regular intervals. 新宿にある彼のオフィス nests a relative clause (新宿にある 'that is in Shinjuku') modifying オフィス. Three に particles in one sentence, each with a different function: interval, existence, and destination.