You can try this route -- I do it regularly from route 206 north of Princeton:
* Drive over the Outerbridge, take the West Shore Expressway to Arthur Kill Road exit.
* Park right on the service road / exit ramp (lots of people do), and walk past the traffic light to the bus stop.
* Take the x19 to downtown Manhattan (30-60 minutes depending on traffic).
* Hop off the bus and take the subway to Brooklyn -- the 2, 3, A, C, N and R trains are all available in the first three bus stops in Manhattan, and Metrotech is only a few minutes away on the subway.
If you sign up for the Port Authority EZPass commuter plan, the bridge toll will be around $5; the express bus is $6 each way and you transfer free to the subway. Parking on the street is free.
It's not a bad trip -- it's all highway in your car, the express bus is a comfortable ride and usually plenty of seats, and the subway trip is fast. If you do it regularly and you're on the 206/287 corridor, and you're interested in carpooling, let me know.