Williamsburg is very crowded. It's a predominently Hasidic Jewish neighborhood, and the families have an average of 7 children, and 90% of those children stay in the neighborhood when they get married. It's a lovely area, though, even with so many people.
Bensonhurst is on the other side of Brooklyn, in the south, and it's also getting crowded. The one good thing is that buildings and 3 family homes are going up everywhere over there, so residences are becoming plentiful. Shopping is great there.
Bay Ridge, in my opinion having lived in Brooklyn my whole life, is the best neighborhood. The only issue here is with parking, as in hard to find a spot. But this neighbor has everything, shopping, safety, the Verrazano Bridge as a backdrop, low crime rate, a nice mix of houses and apartment buildings, a big park (Owl's Head, which the locals call Bliss Park).
Mill Basin/Marine Park is also in south Brooklyn, and is where I currently live. I like it here, not too crowded, close to the parkway for easy access to Queens, Manhattan, and Staten Island (NYCs other boroughs). Very close to JFK airport.
Park Slope, Brooklyn Heights are sort of Yuppieville, the Young Urban Professionals. It's full of historic brownstones and lots of families. Well, every neighborhood in Brooklyn really has lots of families. This particular area is close to the Brooklyn and Mahnhattan Bridges, and also to Downtown Brooklyn where the courthouses are. It's actually a very vibrant, exciting area, crowded though. But not in a bad way.
Don't worry about your relatives moving to Brooklyn. It's a great place to live, no kidding. And I'm so happy that I raised my kids here. No offense to anyone, but I think it's an advantage to come from Brooklyn.
If you have any specific questions, please ask. I love talking about my Brooklyn!