The first thing to note is that electronic mapping programs are not great for estimating travel time. A computer doesn't have the need to eat and sleep or to fill with gas, never mind other real world problems such as road congestion and construction. In other words you won't get from Chicago to Steamboat in 18 hours, but you could still do the trip in 2 full days of driving between 10 and 11 hours with appropriate stops. Grand Island NE would be a good target for day one with an early start. It would be another 2 days of driving direct to LA, with Springdale UT being a good days drive which is a lovely town on the doorstep of Zion NP and to do it justice, you would need to spend a full day in the park. From Springdale you could drive direct to LA. Yes, there are plenty of other options, Rocky mountain NP, Arches, Canyonlands, Bryce canyon, Grand canyon and many more but only you can decide which you want to see and whether or not you want to add a day or two to make it possible to include much else.