The Cambridge Grammar of the English Language (pages 1248-1249), "hollow to-infinitivals licensed by an attributive adjective":
[i] London is an easy place to get lost in __.
[ii] The price was a difficult one to better __.
These initial examples bear a clear resemblance to the construction just discussed: they are comparable to "London is easy to get lost in" and "The price was difficult to better". The applicability of the adjective is contingent on it being construed with the infinitival: [i] doesn’t say that London is an easy place, but that London is a place which it is easy to get lost in. Likewise in [ii] it is not a matter of a difficult price, but of a price that it would be difficult to better. It makes sense, therefore, to treat the infinitivals here as indirect complements in the structure of the NP: they are licensed not by the head of the construction, the noun, but by a dependent of it, the attributive adjective.
Did I understand correctly that:
In [i], the object of the preposition "in" is not the noun phrase "an easy place" but the noun phrase "a place".
In [ii], the object of the verb "better" is not the noun phrase "a difficult one" but the noun phrase "one".
an update:
It seems to me to consider the subjects ("London" in [i] and "the price" in [ii]) the objects of the non-finite clauses is incorrect because (according to nschneid's answer below) there is an analogous sentence where there is not such an opportunity:
(3) Such an easy place to get lost in __ should have more signs.
What is the object of "in" in (3)?