KOA's are usually very nice..if a little pricey compared to other campgrounds. BUT, I have kamped ;) there a lot with kids. There is usually a pool, laundry, showers, etc. and makes for a nice place to stay. I also usually felt safe--lots of families and kids and nice grounds. You might alternate in and out of them to a less expensive accommodation in between. KOA's national headquarters and the very first KOA is in Billings, MT :)
Whoops - here I thought I had had the complete thread-killer experience, but you two have also given some great advice.
I think I will do the one night thing too, 100%mom, and look for something around Bozeman.
Momsteader, this is really good info. about KOAs. I'm not looking for a pool at all, but I've heard that the KOAs often have enough spaces that you won't be turned away if everything else is full. I will keep these in mind.