If your intent is to get from point A to point B as quickly and efficiently as possible, I-70 to I-40 is your best bet. You're far enough south to dodge the Rocky Mountains (and the altitude and possible snow) and it's interstate all the way. You won't hit a lot of big cities, but some highlights along the way include St. Louis and a quick side trip to the Grand Canyon.
The Stats: 2,777 miles in 45 hours
The Northern Route:
For the northern states sightseer, taking I-80 to I-90 to I-15 will slow things down significantly but take you through Chicago, past Mount Rushmore, to Yellowstone National Park, then southward through Vegas before hitting Los Angeles.
The Stats: 3,241 miles in 54 hours
If scooping down south is more your style, I-81 to I-40, 30, 20, 10 is the way to go (especially for art and music lovers!). You'll get to hit Nashville and Memphis along the way, see all the great art museums of Dallas/Fort Worth, and even pass by Donald Judd's remote Chinati Foundation before skimming the Mexican border and heading on westward to LA.
The Stats: 2,987 miles in 48 hours
(Image: USGS via University of Texas Libraries, photoshopped by Regina Yunghans)