I'll start off by rating the two states I am most fimiliar with, South Carolina & Maryland.
South Carolina (grade: D)
I would give my state a total F based that almost zero roads here have shoulders nor are bike friendly on the major roads. Many roads are also narrow two lane here. The only reason I don't give it a total F is that there is many back roads that are lightly traveled. Other than for dogs, they are good for riding. They are also requiring that new roads have at least a two foot paved shoulder on them.
South Carolina has an unofficial bicycle route map at:
Maryland (grade: B)
Outside the Baltimore-Washington metro area, the bicycling is outstanding here. Most of the major state routes have wide nicely paved 8 foot wide shoulders. You also have a good many bike-hike trails here. The C&O Canal is outstanding. Getting into Baltimore can be a pain if you don't know the road well along with bad neighborhoods. Traffic cutting into you or across you can be a pain in busy metro areas. Baltimore's light rail is very bike friendly as is the DC Metro (finally) Sometimes during bad winters, potholes can be a problem.
http://www.bikewashington.org is an excellent site for bike routes in Maryland
The state of Maryland also will send you a free bicycle map of the state
Like to read some opinions about other states
Happy Miles and Cheer,