Duluth and the North Shore is surprisingly pretty. If you fly into MSP, its about a two hour drive to Duluth. There are a number of lakeside "condos" that can be rented. Rock climbing. Fishing. Pretty waterfalls. Glensheen to tour. And pretty cheap! The Twin Cities is a really interesting place - you won't lack for things to do here - we have a great children's museum, two great art museums, a world class theatre, most major sports leagues....
My favorite US city to visit is San Franscisco. Its the only place in the US I've been where I feel its completely different from the rest of the US. With kids there is Muir Woods, Alcatraz, the Exploratorium. It isn't a great city for a four year old, but the older two will love it! (Get tickets to Alcatraz in advance). Downsides - SF isn't cheap.
Mammoth Cave is another fun one (if your four year old is a walker). Like Alcatraz, get your tickets in advance for cave tours. In that neighborhood is Nashville and Lexington/Louisville.
If your kids can handle museums, all American's (whoever they are going to vote or not bother to vote for) should get a chance to visit Washington, DC.