Long but leisurely trip from NH to NM up to MT then home

For that kind of trip I would not make reservations so that I did not have to be at a certain place at a certain time. But at the same time I would not expect to get into national parks, some state parks, and any other very popular park with last minute try. But if you are flexible, and sounds like you are, you can find something at least within a reasonable drive. May not always be something you would prefer, but doable.

I would only make a reservation if there was a specific place I really really wanted to stay.