Do you know any restaurants which I can eat local dishes? ではダメですか? → ダメです。
理由:
〇Do you know any restaurants [at] which I can eat local dishes? ← ①Do you know any restaurant? + ②I can eat local dishes [at] them(=restaurants). ※at them(代名詞) ⇒ at which(関係代名詞)
〇Do you know any restaurants where I can eat local dishes? ← ①Do you know any restaurants? + ②I can eat local dishes there.
※there(副詞) ⇒ where(関係副詞)
参考にしてください。
関係代名詞か関係副詞の違いですね
授業ではwhoでしたが、whoでもいいのですか?