Financial District itself is a booming area for young professionals. You have the seaport with historic Front Street and Stone Street. Both areas are great for happy hour and brunch. As for nightlife you have to venture elsewhere but you are very close to Tribeca, Soho, LES, Meatpacking, East village, and West village. All exciting neighborhoods to eat and drink. I've personally lived and worked in the Financial District for 5 years and love the area itself and the accessibility to other sought after downtown neighborhoods. You have both east and west bounds trains right here so you can get anywhere you need to in the city and still come back to a quiet neighborhood and a luxury doorman building at night without paying a premium for location in rent.
Besides the immediate neighborhood, Battery Park and Tribeca would be your best choices if you wanted to walk or take a short train ride to work. Battery Park City is almost all residential space with a lot of green space and no construction noise. Tribeca is one of the most sought after (and expensive) downtown neighborhoods because of its retail, ambiance, architecture, and exclusivity.
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