The Financial District is an area at the southern tip of Manhattan. Major sights include South Street Seaport, Wall Street and the New York Stock Exchange, Battery Park, Trinity Church and the Woolworth Building.
The financial district is enjoying a rejuvination - like the remainder of the city - and more and more residential developments are planned. The following link provides a list of new developments:
I've got colleagues that live in the area and they love it. I love walking through it... the buildings are imposing, beautiful and the streets narrow.
If you're thinking about moving there, I highly suggest you visit first, and spend a day of it. It's easy fall in love with different parts of the city.