We never make reservations. When traveling around the state, we will call an RV park we find in the Woodalls Directory a couple hours before we plan to stop, and make sure there is a spot for us.
If you want to use State Parks or Forest Service campgrounds, most of them do not accept reservations. More often than not, the contact number will be a Ranger Station several miles from the campground, and nobody there has any idea what the current status of the campground is.
Another thing to be aware of is that very few of the State Parks or Forest Service campgrounds have any dump stations. If you use a "blue tote", be sure there is a place to dump it BEFORE you fill it! There will often be one vault toilet and one water faucet for each 5 or so campsites. There will be no lights and no electric power available. There will probably be no bath house or showers. There may or may not be paved interior roads and sites. Be sure to read the rules posted on the entrance signboard. Dumping your waste water in the vault toilets is often forbidden, but some places do allow it.
Please, be VERY careful with fires. Pay close attention to the posted fire dangers and fire restrictions.
Let me know if you get close to Billings.
