Brooklyn

The borough of Brooklyn used to be (and still feels like) a separate city, which partially explains the reason why it's laid out the way it is - with its own "Downtown", for example, as well as mirror images of some of Manhattan's features (e.g. Prospect Park playing the same role as Central Park in Manhattan).

NORTH-WESTERN BROOKLYN

Brooklyn neighborhoods that make news most often (real estate-related or otherwise) are all in the north-western section of the borough:

• Boerum Hill
• Brooklyn Heights, Brooklyn's own version of the Upper East Side (that is to say, most Wall Streeters who happen to prefer living in Brooklyn opt for Brooklyn Heights)
• Bushwick - the new frontier of hipsterness in the city. Still a poor neighborhood, with relatively cheap rents and plenty of old industrial loft space.
• Clinton Hill
• Downtown Brooklyn Brooklyn's business and commercial hub that still doesn't feel very neighborhoody. Give it a few more years.
• DUMBO (=down under manhattan bridge overpass). Brooklyn's version of SoHo, known for its loft buildings, resurgent nightlife and awesome views of downtown Manhattan across the East River.
• Greenpoint - slightly more removed than its hip cousin, Williamsburg (due to the necessity of changing trains when commuting to/from Manhattan), Greenpoint wins in the cheaper rent deparatment and is generally more tranquil than its hip neighbor to the south.
• Park Slope known for beautiful brownstone buildings, wide avenues and neighboring Prospect Park. Hence, baby-stroller central of New York.
• Williamsburg - the housing stock (particularly old buildings) is not necessarily that good, but the neighborhood wins with its combination of trendiness and small-town feel.

CENTRAL & SOUTHERN BROOKLYN

Further down south are neighborhoods that feel more ethnic, less densely built up and sometimes less "urban" (this is a generalization, though because some sections of Southern Brooklyn are very much high-rise):

• Bay Ridge
• Bensonhurst
• Brighton Beach
• Clinton Hill
• Crown Heights South
• Homecrest
• Flatbush
• Lefferts Gardens
• Midwood

EASTERN BROOKLYN

• Brownsville