"Neck of the woods" is a colorful idiom that refers to a particular geographic area or region. However, as an idiom, it does not have antonyms in the traditional sense; it cannot be directly translated into the opposite meaning. Instead, one way to provide contrast to the sense of regionality and familiarity that "neck of the woods" conveys is to use words that suggest distance or foreignness, such as "far-flung," "unfamiliar territory," or "distant lands." Alternatively, you could use related idioms that imply different degrees of closeness or familiarity, such as "out of my league" or "not my cup of tea.