Manhattan

[foxlair]

What is the residential Quarter of Lower Manhatton known as

[Fibonacci]

Harlem

[shaneystar2]

Brooklyn Heights perhaps.

[pega]

Having been to New York seven times not sure what you are asking here, need to be more precise as there are boroughs in Manhatten which have been given as answers
Lower Manhatten is near Battery Park and the river, includes wall street etc. and this area is known as DOWNTOWN if this is any help I have walked many miles in NYC and please god I'll be able to go again and see the new building when Ground Zero is built up

[Vimto]

The Bowery.