The original is fine: I need a place to rest. I need a place to go. I need a place to sit , etc.
— Mister Micawber
The original is fine: I need a place to rest.
I need a place to go.
I need a place to sit , etc.
I cannot tell you why the preposition is lost, however, though it does have to do with 'place' since we need the preposition with other nouns: I need a cushion to rest on.
I need a home to go to.
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The original is fine: I need a place to rest. I need a place to go. I need a place to sit, etc.
I cannot tell you why the preposition is lost, however, though it does have to do with 'place' since we need the preposition with other nouns: I need a cushion to rest on. I need a home to go to. I need a chair to sit on.