I used to commute from westchester county into midtown, and there were definitely parkways in, although I never needed to go all the way down to Manhattan itself. I would usually try to take the train though (often not possible given how westchester county is poorly connected to train stations).

Because 405 is already a a crowded route that becomes bogged down during rush hour(s). Your choices are pretty much sound, city, lake, city, or mountains if you are looking for a route through Seattle.

How do you get from the GW bridge to the Cross-Bronx Expressway if there are no major highways through Manhattan?

278 also runs through Manhattan. I assume the previous poster really means something that excludes Randalls Island and the Heights.