I've driven east-west from the midwest to the west coast on I80, 90 and 94.
First, I echo the previous poster about taking more time if possible. The western states are enormous.
90 across S Dakota is the most scenic route. It's also going to take the longest as there is a lot to see on this route. You absolutely must drive 90 through western MT and northern ID at bare minimum. I'd recommend a few days of camping/hiking/driving in these areas. You can drive through an awesome mountain pass at huge elevation if you go south from Billings to Yellowstone. I would also recommend driving the highway along the Columbia River on the OR/WA border.
94 in N Dakota provides a stunning test of will because that state is so flat, so large and almost entirely empty. You'll hate this drive while you're making it, but you'll never forget it either if you do it. You'll make the best time this route as there is simply no reason to stop in ND other than getting gas and seeing T Roosevelt national park near the MT/ND border.
Drive 80 if you want your kids to sense the magnitude of the farming operations in this country. More population and towns than I94, but nothing compelling to stop for in IA or NE. Driving across Nebraska is also a test of will. From here you can go through Denver and SLC which are spectacular drives, and you'd drive through the salt flats (which is like another planet) in UT if you drive west on 80 from SLC.
As far as cities, Chicago is the must see city outside of the coasts if you pick one. Rush hour there is nasty, so time it accordingly if you want to drive through downtown. IMO you shouldn't spend much time there on your trip since it's so easy to visit by plane over a long weekend. For about $100 admission total for the family plus parking you could see the Art Institute, which is one of the best. Get a Chicago dog, Malnati's deep dish and some Italian Beef and you'd be out of there in under 4 hours for under $175 total.
Have fun!