1. Where does Tom live? In Shibuya or near it?
If he lives near the area of "Shibuya," then you would say "Tom is an English teacher who lives near Shibuya." Or "...close to Shibuya."
You wouldn't use "nearby" in that sentence, unless you were trying to say that he lives in Shibuya and Shibuya is nearby to where you presently are. "...teacher who lives in nearby Shibuya."
2. You need to say "...close to the palace" or "...near the palace."