Thanks for the feedback. While I'm going to Manhattan - it is lower Manhattan so I guess that's why google maps routed me through the rockaways. I also tried RideTheCity maps and they pretty much agreed with the google routes - I suppose it's since they can keep you on either designated bike paths, or bike lanes to a larger extent.
Anyway - I searched for the Montauk Century route and found someone who had ridden the whole thing from Manhattan to Montauk. It looks like I could pick up that route in Lynbrook on E. Merrick Rd > W. Merrick Rd > Merrick Blvd > Jamaica Ave > Metropolitan Ave over the Williamsburg Bridge. I'll have to plug this route into map my ride or something to see the distance.