If unofficial neighborhoods count, I’m thinking a lot of cities will qualify or come close.
There’s a North Philly, a South Philly, a West Philly, and a Northeast Philly.
And Boston has the North End, South Boston, the South End, East Boston, and the West End. Though their actual locations bear little resemblance to their names…
New Haven,CT is bordered by the towns of North Haven & East Haven, and the city of West Haven.
No South Haven, though
There was Montreal East, West, North, and South. East and West remain as independent municipalities; North became part of Montreal (remains by name as a borough) in 2002; South remained independent until 1961, when it merged with Longueuil.
Geographically - “West” is almost directly south of “East”; “South” was more or less east of “West”; “North” is just to the west of “East”. Montreal remains in the middle.
Apparently at one point, the New Haven neighborhood of Morris Cove wanted to break off to form a proposed South Haven. So we almost had all four compass points.
London, England has North London, South London, East London, and West London, surrounding Central London and the City of London. (Plus the East End and West End.)
Likewise, New Jersey has the Oranges (East, West, South, but no North) and the Caldwells (West and North, but no East or South).
Don’t know if this counts but the small town of Lebanon, Maine includes the villages of Center Lebanon, West Lebanon, North Lebanon, South Lebanon, and East Lebanon
So South is north of Center. Got it.
Jeebus Christ; can’t anybody there play this game? 
Y’know, I think I’ve been corrected on this once before. But my memory is soup, so there’s that.
Well, we’ve explored the 4 trivial roots - any areas that really step up their game and box the compass, even if only in small part?
No Old Haven?
That was the stand-in for Martha’s Vineyard in The Ghost Writer.
There’s a town in Vermont called Westminster, it contains the villages of
That’s got to be worth something.
Way back in 2016, I found what may be the best answer of all here.
In Victoria, Australia there is the ordinal full house of Melbourne (postcode 3001), North Melbourne (postcode 3051), South Melbourne (postcode 3205), East Melbourne (postcode 3002) & West Melbourne (postcode 3003).
Bit further north in NSW there is Sydney (postcode 2001), North Sydney (2060), South Sydney (postcode 2015), East Sydney (postcode 2010) but there is no suburb of West Sydney.
That’s really a doozy. Great cite.
I get that the NW suffix refers to the quadrant of the larger city. If you (anyone) zooms in, or better yet clicks the “view larger map” to get a full-sized tab, then zooms in, the naming of the streets in that whole small diagonal subdivision is just insane.
I’m surprised the city or county authorities permitted those streets to be named that way, and those houses to be numbered as they are. Sure not conducive to quick sure emergency response to the correct address.
Historically, Yorkshire, England was divided into “Ridings” (Thirds), but now exists as the ceremonial counties of North Yorkshire, South Yorkshire, West Yorkshire, and the East Riding of Yorkshire.
There are the Brunswicks in New Jersey. There is North Brunswick (I used to live there), South Brunswick, East Brunswick, and New Brunswick. No West Brunswick though. I always liked that North Brunswick was south of New Brunswick.
Manhattan has the Upper East, Upper West, and Lower East Sides. A few real estate developers tried rebranding Battery Park City as the Lower West Side, but it didn’t stick.
Washington DC has streets officially designated NW, NE, SW, and SE depending on what direction they are from the Capitol building.