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When can I omit the preposition in this type of sentence?

New York is a horrible place to live (in).
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I have seen it informally used without the proposition.
New York is a good place to grow up.
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AnonymousWhen can I omit the preposition in this type of sentence?
I have never seen a satisfactory answer to this question.

You can live somewhere. (no preposition)
Therefore, place to live is possible. (no preposition)

You can live in a place. (preposition)
Therefore, place to live in is possible (preposition)

By extension, any intransitive verb will do: place to work (in), place to sleep (in), place to play (in), ...
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Remaining with places, you have the expressions somewhere to go and somewhere to go to. As above, somewhere replaces the entire phrase that says where one is going, for example, to the movies.
--I'm going somewhere.
--Where?
--To the movies.

Or it can replace only the object of the preposition, for example, the movies.
-- Where are you going to?
-- The movies.

Consequently, you have the choice between such sentences as We have nowhere to go and We have nowhere to go to.

We have nowhere to go -- not even to the movies.
We have nowhere to go to -- not even the movies.

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You said "in this typeof sentence", and that's where the trouble begins. Emotion: smile
I don't know if there is a general rule.
Here's another example:

You can ask something. (no prepositiion)
Therefore, too much to ask is possible (no preposition)

You can ask for something. (preposition)
Therefore, too much to ask for is possible (preposition)

So the preposition for can be included or omitted in Do you think it's too much to ask (for)?
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Each verb and preposition combination must be examined separately, I think, to determine whether that preposition can be omitted or not in any given sentence.

CJ
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Any help?
 AlpheccaStars's reply was promoted to an answer.
AnonymousWhen can I omit the preposition in this type of sentence?
New York is a horrible place to live (in).

I would say 'in' can be omitted, as the following examples from BNC show:

APL 25 must be the worst place to live.

CFJ 135 We must all do everything we can at all times, to make Riverbank a better place to live.
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It sort of feels like if you don't use the 'in' then you are implying that the sentence is incomplete because you're not including living within New York...I don't know if what I just said made any sense.
 CalifJim's reply was promoted to an answer.