One of the most daunting subjects when planning a first tour seems to be the choice of scenic, safe roads (maybe only if you are from California). This should not be the case, as there is a multitude of suitable roads out there. The good people at Adventure Cycling produce very helpful maps of their many cross-country routes and the Great Divide Mountain Bike trail. For additional information on specific roads that I have toured, see the U.S. Tour Map.
While following someone else's route would certainly provide you with an excellent adventure, do not be afraid to chart your own course and go where you want to go. Start by contacting the Departments of Transportation for each of the states you will be going through. Many states produce bicycling maps which detail road conditions including shoulder width, grades of mountain passes, and amount of traffic. These come in handy, but the foolproof way to choose your route and insure a meaningful experience is to travel through the smallest towns you can find. With the exceptions of the east and west coastlines, large areas of rural land are everywhere and are excellent for cycling. Some of these roads may seem like they were built in Roman times, but the scenery, lack of traffic, and hospitality of people might just be the highlight of your trip.
Whenever possible, talk to locals about road conditions, short-cuts, and interesting sites that only they will know about. Be aware that "the next town is a couple of miles down a flat highway" could mean twenty miles on a very rolling, badly paved road that may turn to dirt. When passing through medium to large cities, there are usually certain roads with much less traffic; ask locals about these or check out a regional map.
Riding through major mountain ranges should not be feared. They do slow your rate of travel, but they are often the most beautiful sections of a journey and offer the best camping. The amount of work you expend on an ascent will be paid back tenfold with feelings of accomplishment and miles of downhill cruising. Definitely worth a little sweat.
In most states it is illegal to ride a bicycle on Interstate highways
if there are other roads you can travel on. Large highways are usually
loud, flat, straight, trash-filled strips of semi-trucks anyway; you
do not want to be there. Remember, bicycle touring is about experiencing
movement not just the destination. Choose the right roads, and you won't
care where you end up.