https://www.quora.com/Why-do-Americans-sing-Country-roads-take-me-home-to-the-place-I-belong-instead-of-Country-roads-take-me-home-to-the-place-I-belong-to-Is-that-a-regular-grammarIt is correct grammar.
You do not belong to the place. That would mean the place owns you. You belong there because it is an appropriate place for you. Nothing wrong with the grammar.