Depending on what your budget .
If its in 1.4m range Clinton Hill
if its in 800k- range Bedford - Stuyvesant
if its in 600k- range Bushwick
These neighborhoods coming up but there are good areas to raise a family. If you have the ability to buy in Clinton Hill, Park Slope,Fort Greene... its the best area in Brooklyn
Regarding the "best neighborhoods to raise a young family" I would say that it depends upon what is most important to you. As licensed real estate agents, we cannot steer you toward a particular neighborhood for a variety of legal reasons. I would suggest you do some research onlne and then visit the neighborhoods that interest you the most. Do you want to be where the schools are top-rated? Then research that. If you want to be where there is the most concentration of cultural institutions, then make that your priority. There are many aspects to evaluate to decide what is "best" for you. I personally raised my family in Park Slope, Brooklyn. That is my own experience. I have sold apartments throughout Brownstone Brooklyn as well as all over Manhattan to people of all family statuses. "Best" is in the eye of the beholder. Here is one article you may enjoy rating what New York Magazine considered the top neighborhoods in NYC:
Best is really a matter of personal preferences, financials, wants, needs, lifestyle, etc.; therefore consider visiting areas of interest more than once and at different times of day; possibly chat with locals, look at everything that is important to you, etc., then determine wher your comfort level will best be reached. http://www.homefair.com/
There are many factors to consider: school ratings, proximity of parks and playgrounds, etc. etc. If you would like to discuss your needs in great detail, Muffinman - feel free to call me at 646 256 0899.