Aplogies in advance, I lack the specific terms to describe the concept, but bear with me!
"Vicinity" needs to belong to something. Using the first example:
There are a few hotels in the vicinity.
There's an implied "of the [object]" on the end, e.g.: "There are a few hotels in the vicinity of the beach". This means that although in some cases it can be implied and thus hidden from speech, it's always "in the vicinity of [object]".
With that in mind, and how "vicinity" needs to be posessed, you would say "in the station's vicinity", or "in the beach's vicinity" going back to the previous example.
Further, although most people drop the possesive when saying "city centre", I think that it's actually "city's centre", just like you'd never say "the staircase is at the building centre", but "the building's centre". As such, "vicinity" can be used in the same way -- posessively.