Learn English – “within 1 to 2 weeks” vs “in 1 or 2 weeks”

SHORT ANSWER: It modifies neither.

LONG ANSWER:
This is actually a more complicated matter than traditional grammar can handle.

1. Neither of these two preposition phrases^† really modifies the verb hung. Verbs like this one are called ‘linking’ or ‘copular’ verbs because they link the subject to a complement which describes the subject—a subject complement.

   The most common copular verb is BE, but there are also verbs of perception such as appear , seem, sound, look, taste which ordinarily take adjectival complements describing how the subject is perceived, and verbs of location which ordinarily take ‘adverbial’ complements describing where the subject is to be found. In this case, intransitive hang takes in the air above the city as a subject complement.

   Note that transitive hang similarly takes an object complement: in the sentence “He hung the bag on a hook”, the preposition phrase ‘modifies’ the Direct Object bag, tells the location where the bag is to be found.

   For this reason I have to dissent from Nico’s characterization of this as a dangling modifier; it is both semantically and syntactically quite unambiguous what is where.

2. As for the sequence of two preposition phrases ... I’m talking off the top of my head now, and I think it likely that modern grammars have a more incisive description of what is going on here. But it seems to me that the second phrase does not so much ‘modify’ or qualify the first as it supplements it. This works rather like chained adjectives before a noun: in the phrase a big red box, big does not qualify red, it provides additional information.

   However, as Nico quite cogently tells you, it doesn’t really matter how you parse the sequence. You could flip this to above the city in the air and it would not change the sense. By and large, however, we prefer to order the phrases as you have it, moving from the more general location to the more particular.

^† The reason for calling this a “preposition phrase” rather than a “prepositional phrase” is treated here.

Here are some empirical results.

Corpus Of Contemporary American English:

• WITHIN THIS WEEK: 2 hits
• BY THE END OF THIS WEEK: 58 hits

BYU-BNC: British National Corpus:

• WITHIN THIS WEEK: 0 hits
• BY THE END OF THIS WEEK: 7 hits

We can conclude from that that "by the end of the week" is much more common in both American and British English, and thus it is also probably much more natural.