When we say "to live in the place," there is a preposition "in." Therefore, when "to-V" becomes the modifier of "the place," the preposition "in" should also be there to complete its function--thus "the place to live in.'
However, the teacher's manual I'm using (in Taiwan) has the guidelines that say "when some specific nouns like 'place, day and time' are used, the preposition can also be omitted."