Mount Rushmore is one of the places in the U.S. you should visit at least once. It is really amazing! It seems unreal how one person can do such a huge thing! We did not have much time when we went there. We just took some pictures with the Mount and did not go close to the monument. However, we had a chance to go to the Borglum Historical Center in Keystone, SD day before. It was really nice to know the history of the mount as well as some info about the person who carved it.

Wind Cave National Park is the place you want to go with your kids. It is a unique opportunity for kids to see what it looks like to be inside a cave. Kind of remind me of Tom Sawyer adventures  Tours are scheduled every one hour, so you do not have to wait long. Then a guide will take down the cave. It is not actually dark there. There are a lot of lights installed in the cave. The walk is not very long so little kids do not get bored. However, I would not recommend taking very small kids. They may easily get scary.

Knife River Indian Villages is a historical complex dedicated to the live of the Northern Plains Indians. The complex starts with the visitor center where you can watch a film about Native Indians, there history, traditions and the way of live. Then you can walk to a reconstructed earthlodge village and Sakakawea Village site. It is very spiritual to walk there. It makes you think about these great people who were living there. Just imaging living whole North Dakota winter in the a earthlodge!
The place is more siutable for families with bigger kids like 5 and up. Although, you have to do a lot of explaining. We went to visit the village after we read a book about Lewis and Clark. So, it was very natural for our kids. Also, they were excited to see how Fighting Sioux lived back there.
On the downside, I should say, there is not many places around to eat. So, make sure you pack a snack with you.

Turtle River State Park is only 20 miles from Grand Forks which makes it very convenient to go there with kids for a day of fun. There are varieties of activities you can do there: camping, picnicking, fishing, hiking, mountain biking. It is not very suitable for swimming. However, it is a perfect place for a picnic. We used to take our kids there for a nature hunt. It is very educational. Depending on the season you can get different plants for a herbarium. Also in the winter (which is very long in ND) you can go there for cross country skiing. Children love to ski there because it is not too busy.

North Dakota Museum of Art is located on UND campus. It is small but very nice museum. It is easy for kids to go to a small museums so they do not get bored. Museum features work of various authors from North Dakota as well as from around the world. The best thing there is the music which is constantly playing on the background. Sometimes, it is even a live music. It adds such a dramatic effect to the paintings. There is a cozy café and a small gift shop as well. Outside the museum, there is a garden with some sculptures made by UND students. It is really cool and my kids just LOVE to walk around them and guess what is it:)