Moving to Brooklyn...but where in Brooklyn?

Hello! I'm planning on moving to NY in the coming months. Although I've decided to reside in Brooklyn, I'm not sure where in Brooklyn is the right choice. I'm a single women who will be living with roommates and would like to find a safe apartment that is close to reliable public transportaion to get me into Manhattan during the week, a grocery store, and a laundrymat. My maximum for rent is $2,500. Is all of that possible here in Brooklyn? If so, are there better options tthan others? Any advice or suggestions would be much appreciated. Thank you!!