I suggest you consider the following:
Start in San Francisco, spend 4 days there, then spend 7 days driving down the coast to San Diego (see my other post to cuddlekez entitled "drive san diego 2 san fran", but just reverse the order of that trip--and take an extra 2 days in Los Angeles, and 1 extra in San Diego).
From San Diego, either drive or fly to Las Vegas--I suggest drive so you can see the desert here and understand how vast it is.
Spend a day driving to Sedona, Arizona, then another day going to the south rim of the Grand Canyon, then another day driving to Page, Arizona through the Navaho Indian Reservation and seeing Lake Powell in Utah, one day to go over to Monument Valley and one day back, then one more day back through Zion National Park to Las Vegas. Then spend 4 days in Las Vegas. Drive back to Los Angeles, spend your last 4-5 days there, then fly home.
Monument Valley and Lake Powell is the closest thing to a true western US experience you can find--Monument Valley is the place where most US westerns were filmed because of it's amazing backdrop--and was even featured in the second "Mission Impossible" movie--where you see Tom Cruise climbing the side of a gigantic mesa at the beginning of the film. Lake Powell has the most amazing river/lake scenery you will ever see anywhere. Here are three pictures--the first of Monument Valley, the second of Lake Powell, the third of Sedona:
http://www.astronomynotes.com/nature/shoffner/MonumentValley3.jpg
http://www.spinosa.com/lake_powell.jpg
http://www.fineartphotoblog.com/wp-content/uploads/sedona-ridge-800px.jpg
To give you some sense of perspective, there is a boat in the second picture above. The boat shown holds 50 people and is taking them to see the famous "Rainbow Bridge Arch" that is 40 miles farther up the lake. (The lake is over 250 miles long).
You could also take a day to go see Death Valley (from Las Vegas)--and you could also take a 2 day trip from San Francisco to see Yosemite National Park (although most of it is closed in the winter), and possibly Lake Tahoe.
Here's a Death Valley picture:
http://www.eugenecarsey.com/camp/deathvalley/deathvalley01.jpg
Enjoy--no matter what your choices are