Manhattan Island in the mid-19th century would have been fundamentally recogniseable, its familiar grid system in place, though some of Melville's phrasing shows its age. The "noble mole", a breakwater protecting a coastline against the open sea, refers to Battery at the southern tip.
Corlears Hook was a disreputable area of the Lower East Side (supposedly the origin of the term 'hooker'), and to pass from there to Coenties Slip and northwards via Whitehall Street would take you around the southern and south-western edge of Manhattan, with a view out into the New York Bay towards the Atlantic.
"Manhattoes" is a popular term for the island's native American inhabitants, from whom it was bought by Dutch settlers in 1626. They were of the Lenape tribe, in whose language 'Manna-hatta' means 'Island of many hills'.