You can legally ride on practically any highway, except for the Interstate Highways (and even in the West, you can ride them if there is no practical alternative).

An easy way to plan a long distance trip is to get one of the pre-planned routes from the Adventure Cycling Association. They have a route down the East Coast - you can buy their maps as a starter:

http://www.adventurecycling.org/rout...anticcoast.cfm

The advantage of their maps is they've already thought through the best routes, and also marked places to stay, campgrounds, and bike shops along the route.

Sometimes the best touring route is a quiet back road...sometimes it's a busy highway with big broad shoulders. The ACA maps are an attempt to strike the right balance.

The other way to do is just get state highway maps, and look for the smallest paved route that's more-or-less direct to where you want to go.

You can also check each state's transportation department - many states of marked preferred bike routes, or bicycle coordinators who post preferred routes. Some states also maintain published traffic volume statistics so if you're planning a route you can choose a road based on observed traffic volume.