My husband and I are into our third week of a Northern Tier tour. We're doing mostly motels and B&B's right now, because it's comfortable. The motels can run anywhere from $65 - $90 per night. The nights we've camped have been state parks, which are about $20 a night. I don't know the pricing for private camp grounds.
As much as possible, we're stopping at grocery and convenience stores for food. For breakfast, we often get an egg sandwich type thing and maybe some juice or coffee. That can be under $10. If you can find a grocery store to make sandwiches for you for lunch, that'll be another $5 - 10. We'll often get one large sandwich and split it between the two of us. Or, you can buy bulky rolls and a 1/3 pound of sandwich meat and make something yourself for a little less. We carry little packages of mustard that we pick up along the way to make sandwiches more interesting. We usually add fruit and some gatorade, another few dollars.
When we camp, dinner is usually mac & cheese with a can of peas or green beans. Going out for dinner has been as inexpensive as $4 for a big bowl of pasta to $50 in a more expensive place, including a few cold beers.
You'll also need to budget for incidentals like replenishing your supply of suntan lotion, toothpaste, etc., replacing equipment and admission fees if you want to stop along the way.
I hope this helps. I've got intermittent e-mail access so drop me a note at firstname.lastname@example.org
if you have specific questions.
As I said, we're just starting our third week and it has been awesome. By all means, you should do this with your son.