Don't miss the J.C. Motel (or whatever it's called these days) in Jerrfrey City, WY. Real swanky.
Was that a joke?
Any way in Jeffrey City the old abandoned Lions Club pavilion is not bad to camp under. It is across the road from the diner. Just use the bathroom and fill water bottles at the diner before they close.
On the TA we camped in town parks and stayed in churches when we could. Both were free. We stayed in inexpensive camp sites when possible and only stayed in KOA type places a few times. The TA maps usually list the options, but we just improvised when off of the route or places where nothing was listed. In the middle of the country you can generally camp in the town parks for free with no hassle. When in doubt ask the local police if the town is big enough to have police.
Ask around if in doubt; librarians, store clerks, wait staff, police, clergy, and folks you meet are all good sources. We never hit a town where we couldn't find a place to stay, usually for free or cheap.
If you get a room always tell them you are bicycling coast to coast and ask for a "cyclists discount" you will usually get one if you ask. Try it at campgrounds as well.
Oh, also stop and compare notes with cyclists going the other way. We got some great leads on places to stay or visit that way.
All that said, I didn't get much experience in eastern Virginia because we stayed with family and friends.