If you do go through St Louis, you can get from the east side to western subs in about 20 minutes, no real traffic. In St. Louis, it is worth stops at the Arch, Anhiser Bush tour, and the Butterfly House...really, the butterfly house is a little know attraction but it is fascinating, unless you are scared of butterflies!
Forgot to mention, if you are are interested in good food, good prices and a throwback to days gone by, try the LEFT FORK Diner in Salt Lake U. Off the beaten path but a local put me on to this place several ski seasons ago. If you can find it, you will enjoy the experience.