The stay at Alex and Shaila's was great. The apartment has plenty of space. It's also spotless and well decorated (I noticed something new everyday). We used street parking with no problems finding a spot. If your looking to stay in Brooklyn this is the place I'd suggest.
The neighborhood is family oriented with a great block party mural on the street. There are several restaurants around but if your looking to go to the park slope or Williamsburg area, I suggest a cab. The subways are not too far away, if you prefer to take them.
Lastly, I was concerned about bed-stuy's crime in the past. I'd say those days are behind it. Some areas still have problems but they are far from the apartment and nothing out of the ordinary for a large city. Use your head, and everything will be fine.