DUMBO is the new SOHO they say; the streets are quiet and industrial, yet full of surprises lurking at each corner. The F train to York Street will take you right there.
Walk down to the water and you'll pass a few cool furniture stores and hit the ABC outlet. Turn left, walk under the bridge, and you'll notice a few hip shops, like Jacque Torres Chocolates, West Elm, etc. There's a great park running along the water with a fantastic playground for kids (shaped like a pirate ship). Keep going and you'll see the old tobacco warehouses, now kept empty, on the park. Beyond that is the River café, the Brooklyn Ice Cream Factory, Grimaldi's, and the Pier. This is a fun little walk that will allow you to walk the cobbled streets and see old tram lines while looking up and admiring the bridge structures.
Take a right in the beginning instead of a left (on Water Street) and you'll run into an Old Manor that was built for the person overseeing the Navy yards. This area, also known as Vinegar Hill, is almost like an old ghost town. Things are changing quickly, as new buildings pop up and the yuppies move in.