Consider:
Smoke hung in the air above the city.
I see lots of sentences containing the structure of "verbal phrase + prepositional phrase + prepositional phrase" like the example above.
I just do not know whether the second prepositional phrase (in this example, above the city) modifies the verb (hung), or if it modifies the noun (the air) in the first prepositional phrase.
SHORT ANSWER: It modifies neither.
LONG ANSWER:
This is actually a more complicated matter than traditional grammar can handle.
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.
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.
smoke hung in a cloud above the city? If above the city would modify hung, it would mean the smoke formed a cloud. If above the city would modify in a cloud, it could be interpreted as a pre-existing cloud holding the ascend of a smoke column.
hang acting as a copular verb precludes interpreting this sentence as a case of dangling modifier.
That is known as a dangling modifier and a source of ambiguity.
In the example Smoke hung in the air above the city the ambiguity is irrelevant, but in other cases the sentence would have to be edited.
Here's an example taken from the wikipedia entry linked above:
I saw the trailer peeking through the window.
This sentence could be understood as either the person or the trailer peeking through the window. To remove the ambiguity, Wikipedia suggests to recast the sentence as:
Peeking through the window, I saw the trailer
above the air modifies smoke hung or in the air. In both cases the smoke will be hanging above the city. I think the example from wikipedia illustrates better this kind of ambiguity.
The sentence says there was smoke somewhere. And where? In the air and the sentence means the air above the city, and not the air above the forest or the lake.
hung in Smoke hung in the air above the city is acting as a copular verb. In simple words, the sentence is equivalent to Smoke was in the air above the city. Without going into the details, I would say @StoneyB made the point that the wikipedia entry on dangling modifiers does not apply to copular verbs. I tried to come up with a good counter-example, but I failed.