try http://www.freecampgrounds.com/ many of the towns fairly close to the freeway in that region have cheap or free campgrounds some even with electric and water. Course they would like you to spend some at their stores but not a requirement.
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When we traveled that route a couple of years ago we found state and local parks along the way in both states that were inexpensive, quiet, had hookups, and not too far off of I80. We traveled from Denver to Chicago and camped two nights each way. For us it was a better choice then a parking lot. Each state's web site will have listings and I believe that there are books available on this subject.
In reference to RAS43's post, state parks along I80 in central Nebraska that come to mind are Mormon Island near Grand Island, Windmill between Grand Island & Kearney, & Ft. Kearny near Kearney, Nebraska. Reasonable rates & IMO much more pleasant than a concrete parking lot.
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On our trip out west this summer, due to some very loud diesel idling at an Iowa rest stop along I-80 just west of Des Moines, we ended up getting back on the road and heading to Atlantic, Iowa, the nearest Walmart. It's about 5 or 6 miles off the interstate, but easy enough to find - we did it in the pitch dark, of course. About half an hour after we parked on the edge of the lot, at about 12:30AM, some kids who didn't have anything else better to do decided to park about 10 feet away and came up and banged on the side of the RV. Scared the hell out of the DW, the three of us jumped out and rained all sorts of hell on the kids. A cop patrolling the lot came over to see what was all the fuss, and told us that he'd be sure to tell their parents. Small town hi-jinks..
No big deal, just another interesting Saturday night in Atlantic, Iowa.. When we woke Sunday morning around 8AM there were already half a dozen cars parked right next to us, out in the very edge of the lot. I thought it was odd. 10 acres of lot, and they gotta park right next to a sleeping RV...
My old territory! There's a very nice private CG on the north side at one of the Amana colony exits. A guy turned his farm into a CG and it's really green and big trees, in the summer. You should find it with a search. The Colonies is also a great tour! Ne. has really nice SP's! Mahoney SP near Ashland Ne. is fabulous! Pioneer Village is near Kearney Ne. and they have primo camping. Pioneer Village is actually a pioneer museum and it's top notch as far as early American articles. They have a lot of one-of-a-kind stuff, from cars to guns to jets to farm equipment. I thinks it's a must-see. I've never stayed at Lake McConauhy at Ogalalla Ne. but it's on my bucket list. Boaters from as far away as Denver swarm that place in the summer.Craig
My home town of Aurora, 30 miles or so east of Grand Island has a VERY nice campground in Streeters Park. Entrance 1/2 mile west of Hiway 34 and 14 intersection , which is 3 miles north of the interstate. They ask for a donation, have electric, best water in the country, and a dump. Next to the city pool, playgrounds and ball fields. Please donate at these type parks to keep them open.
It seems above the Mason Dixon line lots of towns have them.