As far as the island in the mouth of the Hudson River: sorry, it sucks and there’s nothing I can do about it.  This is about the Manhattan cocktail.

The Manhattan is a mixture of whiskey and vermouth, by default sweet (red) vermouth.  The International Bartenders’ Association says:

5 cl Rye Whiskey

2 cl Red Vermouth

1 dash Angostura Bitters

Pour all ingredients into mixing glass with ice cubes. Stir well. Strain into chilled cocktail glass.Garnish with cocktail cherry.

The only real variation on this are advocates of a 2:1 spirit:vermouth ratio and assurances you don’t need to use rye whiskey (you don’t, but more on that).

The problem with this is — at least if your crowd is anything like mine — drinking anything with vermouth in it is sort of like paying black people a fair wage to pick cotton on your farm.  There’s nothing, on examination, wrong with it, but still comes off as a sort of sinister affectation.