Well if this isn't the coolest thing ever! Ride the City. It's not perfect, but it's great. What makes it great is that it gives you both the direct route and the nicest route, with bike lanes. They call it "safest"; I'll stick with nicest. Outstanding. And even when it's wrong, it's still useful. I can't believe I only now just heard about this.
I've already learned, to my surprise, the the most direct route to Lower Manhattan from Astoria is Greenpoint Ave and the Williamsburg Bridge. Craaaazzzy.