I have lived in North Dakota my entire life. So naturally I have a slight bias for some of my favorite things to do in my home state.
1) International Peace Gardens - Growing up in the state, I have visited here countless times from going to camp there as a kid, to bringing my kids there as an adult. It is beautiful. I mean who doesn't want to see a clock made out of flowers?! Ok... Maybe it is one of those things you have to see to appreciate fully. But it is darn cool.
2) North Dakota Heritage Museum - My children (Ages 8 & 6) and I spent HOURS here and a year later they still ask to go back. The Fossils and casts were all cool to see and they were presented with information that made them meaningful. I read the placards while they pointed and talked about how cool the artifacts were.
3) The Medora Musical - I have been here multiple times and it is always a great show and a good time. My sons favorite part was a battle scene... But how can you top that for a little boy that just really likes loud noises and fighting... much to his Mother's horror by the way. *Insert major eye roll. But the point here is, our whole family liked it and my son was the one I thought would be fidgety and unhappy the whole time, but he ended up really liking it.
I have lived most of my life in Devils Lake, ND were out little store is located. So I just don't get all excited when people talk about our AMAZING fishing. I personally, am not much of a fisherman, but it is epic. I hear it on a daily basis... So if you like to fish, it really is can't miss. I personally just like to go for a walk or bike ride along the dike and LOOK at it. Because it is massive and huge and gorgeous. But, as a North Dakota Native I may be a little biased. ;)