The area directly around or outside of a place is called its purlieu. In a sense, a city's suburbs can also be thought of as its purlieus. This word usually shows up in its plural form, as in "the purlieus of the palace."
You can use the noun purlieu for any outlying or nearby areas, or even to mean "usual haunts," like the used record shops and cafes where you and your friends normally hang out. Originally, a purlieu was a term used in Britain's now-obsolete forest law for land adjacent to a forest. It probably comes from the Anglo-French puralee, "a going round to settle the boundaries."