I would like to put forward the following points: 1. "Nearby" can never be a preposition. 2. "Nearby" may be an adjective. He lives in a nearby house. 3. "Nearby" may be an adverb. He lives nearby. 4. His house is near mine. "Near" is used as a preposition. 5. He wants to live somewhere near. "Near" is used as an adverb. 6.. He found a large house in the near distance. "Near" is used as an adjective.

Close to my house.