My friend and me recently went on a cross-country trip from Dayton, Ohio to Los Angeles, CA. We took the Colorado, Vegas route towards LA and returned via Arizona, New Mexico, Texas, Missouri.
If you are visiting Chicago, I would suggest to take the Missouri, Kansas, Texas, NM, AZ route to SFO. Riding through Colorado and Utah using the US-50 was tough. Not to scare you, but it is rightly named loneliest road. We faced severe foggy conditions and there was a lack of rest area throughout the route. It is nothing like the East where we find rest areas aplenty. It can become a bit dull/boring as you drive for hours together. But Utah is a pleasant sight after that tough navigation. I would avoid the wintery places during this time of the season. That is why I am suggesting the southern route.
The Missouri, Texas route is relatively forgiving and is mostly flat. We visited the Grand Canyon but couldn't visit any other place due to lack of holidays :)
We did the whole trip in 6 days (From Chicago to LA and back) while visiting Colorado, Vegas and GC.
Hope this info is of some help.