Google maps has a feature where you can get directions and choose whether traveling by auto, bike or foot. That is where I would start. Also, check the bikely.com website. They post routes provided by cyclists, so they are generally on roads that are safer and more suitable for cycling.

I was trying to figure out a route from Raleigh, NC (where I live), to the coast in the spring sticking to back roads. I used Google maps in bicycling view to find a good route and then transferred the turns to a cue sheet.