The Rails-to-Trails organization sponsors the conversion of unused railroad rights-of-way to hiking and cycling trails, and there are a lot of them, all over the country, and there is an effort being made to connect them up. As far as I know, there is no all-inclusive map of them, but a little time (a lot of time) at this site might elicit a good set of guidelines.

The Adventure Cycling Association sells a good set of maps designed for long-distance cyclists, about which they say Our maps include information not available on typical road maps designed for motorists. For example, the locations of bike shops, sources for food and water, and listings of overnight accommodations (especially camping facilities and small motels) are primary features of our maps. They have a north-south route here that goes from eastern Iowa (not all that far from Chicago) to the New Orleans area. They set up their routes on roads without much traffic and with wide shoulders if possible.

Most Americans are super-friendly and he would probably be overwealmed with offers of meals and accomodations. However, there are a few yahoos out there.