Well, the link below is to a very good webpage about Brooklyn Heights, one of the best neighborhoods in Brooklyn, and the links on the left side of that page will take you to good webpages about some other neighborhoods, too...Good luck!
if you move to brooklyn, i Highly recommend park slope. It gives you a real nyc feeling. very nice neighborhood its near prospect parkso near prospect park is the best place to live. Wow.summer,fall,winter,spring, all beautiful there. If not that, then I would say Bay Ridge, near Verrazano Bridge or Shore Road. You will love it also.those are the top 2, good people and you don t have to make loads to live there, median income.
Outside of Manhattan, Park Slope, Brooklyn Heights, and Riverdale are the nicest neighborhoods.Astoria, Long Island City, Williamsburg, and Woodside are also worth considering.