Check out some of the week-long supported bike tours. There seems to be at least one in every state. They are usually inexpensive and well-organized with routes that avoid traffic and often visit scenic areas. I have ridden Bike Virginia, BRAG (Bike Ride Across Ga), GOBA (Great Ohio Bike Adventure), TRIRI (Tour Ride in Rural Indiana), Cycle NC as well as several in Wisconsin run by POWWOW bike tours. I've enjoyed them all. Generally participants camp out, but you can usually stay in motels if that's your preference. Some of the Southern states have tours that run in the cooler months (Florida, NC), but a lot of them seem to occur in June.