You will be incredibly lucky to find any spot open on Labor Day weekend. If you can camp without electricity or water connections (dry camp), you can look for stores that let you park overnight. Many Walmarts, Cabella's, etc will let you spend the night in a corner of their parking lot. Look at an app like AllStays to find options, and always go into the store to ask them where to park.
Once you get in the "real" west, you might be able to find camping spots not in a campground in a National Forest or on BLM land. You can find information about that from the land managers. Note that these spots too will be very full Labor Day weekend.