As your husband should know, the rest areas and truck stops are crowded with truckers trying to obey the new mandatory rest period regulations and they don't take too kindly to campers spending the night. Walmart's policy of welcoming overnighters has been abused to the point where communities are starting to ban the practice.
This is basically what campgrounds are for. Plan to be in one by late afternoon and stay a night or 2 if there's something in the area worth exploring. Unless you're trying to get into a popular state or national park on a summer weekend, advanced reservations aren't necessary and spending a lunch break on the road with RVParky or AllStays and a phone will be all you need to find a place to stay that night.
If you want to get into Yellowstone, Grand Tetons or Glacier on a summer weekend, you're probably too late to make reservations now. Keep checking for sites that open up due to cancellations.
The further west you go, the easier it will b able to find public land to camp on. Use campendium and Free Campsites to find these.