We would carry the KOA directory and the Trailer Life directory (now it is the Good Sam directory) when traveling like this, start checking a little after noon for overnight stop locations. We would stop at a place that had mobile phone service (much of where we traveled used to be no-service) and call down a prioritized list for same day reservations. Usually we had reservations, or were told we would not need them, before making a the third choice call.
My wife and daughters liked KOA, so those would be the first picks, but that is too limiting. I think 3/4 of the decent RV parks are not part of any franchise, though many associate with Good Sam. Probability of finding a place through much of the Midwest is good, these are not destinations, they are overnight stops.
Busy travel destinations can be a problem. Special events can be a problem. For those, I like a reservation well in advance. Like for Bike Week anywhere, if I want to be there. Sometimes you get caught by surprise; once I found every campsite, hotel and motel room for 50 miles around occupied in a small Missouri town where I often stop. What was going on? Cattle auction. Thus you call ahead same day, rather than assuming there will be space because there is always space.
Holiday weekends can be a problem. So many areas have so few real recreational destinations that they'll all fill up, so just to be camping that weekend families might end up at the RV park behind the gas station at the Interstate exit. This is when all the state parks, COEs, town parks all fill up. If I have to out on holiday weekends, I treat those stops like destinations: reservations in advance.
I have at least three mobile apps for finding and rating campgrounds and RV parks, but still prefer to carry the published directories. I don't find data service everywhere; living in the big empty leaves me less optimistic about always being connected than those might be who live on the coasts or in the crowded states.