Minot is on the lower end of culture as MrChupon said.
The Railroad Museum is a good bet if you'd like to see the history of the railroads as they went through the great plains. Unless you're really into railroad history, it's not that exciting. There's a working telegraph, photographs, not much else.
The International Peace Garden is a little more than a two hour drive northeast of here, you'll see a lot of open country between here and there, small cities and towns, but it's a pretty decent attraction for North Dakota. (www.peacegarden.com) You'll have to pass the Minot Air Force Base on the way there. Either Bottineau or the Lake Metigoshe State Park is close to the peace gardens if you'd like to stay up there an extra day.
The Badlands and the Theodore Roosevelt National Park (North and South parks) are about a three to five hour drive southwest of here. Depending on which park you visit. (
http://www.nps.gov/thro/)
Either of those areas would be okay to visit if you have any free time here, each would take about an extra day to visit.
Other attractions nearby:
Rugby which has the Geographical Center of North America and an old Victorian Dress Museum. About an hour east of Minot.
Right now we're having the Lewis & Clark bicentennial anniversary so if you want to, you can visit recreated Indian villages or frontier forts from the 1800's or trace their trail down the Missouri River.
Bismarck is two miles south of Minot, the state capitol. There's a lot of excellent museums down there and the tallest building here in ND, a whole twenty stories tall. That'll impress you being from CT in your profile.
Fargo/Grand Forks where there's a lot of stuff to do (at least to me) is mostly out of range unless you're going to stay down there overnight (Grand Forks is four hours, Fargo almost five). Both are almost metropolitan areas (over 100,000 people) when you include their sister cities in Minnesota.
Otherwise there's a zoo, some small museums, mostly smaller town items.
The local restaurants aren't that bad, lots of franchises (McDs, Hardees, etc), otherwise there's a small Irish pub/eatery in downtown Minot, Ebeneezers, which has pretty good food. Other ones I like are the Country Kitchen in western Minot, and some of the chinese restaurants.
I'd recommend bringing a book to read, or two, three. Being I'm from here, it doesn't seem any boring to me, but I don't know much don't know how a visitor would perceive it, better to be prepared in any case.