Plus 1 to Jamawani's post except I like shoulders after 3000.
Another source to use are states' bicycle maps. A lot of states still use a pdf of their bicycle map which typically shows the color coded roads indicating the traffic counts and hopefully shoulders. A lot of AADT maps are going to GIS which requires you to click onto each road segment so it takes a LOT longer to determine a route over a large area.
Tailwinds, John