Hi, and welcome to RTA!
I've been the one that's been researching the campsites along the Interstates and the US Highways, and can tell you that "free" is pretty non-existent. There are very, very few, maybe 1% of all the campgrounds I've found so far. Prices range from $8-10 up to $30+ per night. Some are reservable and others are first-come, first-serve. A few are nearby the highway, many are between 10 and 20 miles from it, and a few are further.
Saving money on the road:
Gas/fuel: Get the Gas Buddy app to find the least expensive fuel in the areas you're passing through.
Food: Bring your own breakfast foods for camping, pack stuff in a cooler that you can picnic along the road with. Dinners -- if you're camping, you can get food and cook it on a campstove. On your motel nights, choose a place with a microwave oven and you can make most anything, or visit the service deli of a local grocery store and see what they have ready-made. Carry paper plates and some sort of utensils so you can eat easier in the motel. I've been known to take an electric fry pan and cook in a motel room, but not all folks have room for that stuff in their travel vehicle, and not all motel rooms will let you do that.
Motels: you can use many methods to find one in your budget. We have a Motel Finder on this website (scroll down to the blue section and look to the right). You could use Expedia, Hotels.com, or other discount lodging websites, to find a place. If you're along a freeway, there are coupon books to be had from either a state information/visitor center or from a kiosk at either rest areas or travel plazas/truck stops.
Don't forget to budget for ice!
Donna