Welcome to bicycle touring! Every state has some sort of bicycle map and information via their Department of Transportation. You can see what is available in each state from this page:http://www.pedbikeinfo.org/data/state.cfm
Some of the info is great, some is a bit more spotty.
I'd suggest taking a look at the resources and plotting out a general idea of your route. Then come back here with that info in hand as well as the kind of touring you want to do (hotels or camping? cooking or eating out?) asking your question again. It is sometimes easier for others to respond if they have a clearer picture of what you are looking for and planning.