On your way east be sure to check out the canyon country of southern Utah. Do the "Great Circle Tour" to see Zion, Bryce Canyon, Capitol Reef, and Arches National Parks. Bryce is one of the most fantastic sights in the southwestern U.S.
http://www.nps.gov/brca/
http://www.nps.gov/zion/index.htm
At Bryce Canyon everyone stays at Ruby's Inn.
http://www.rubysinn.com/
Utah Route 12 is one of the most scenic roads in the country. Red Canyon and Big Thunder Road in Dixie National Forest is the inspiration for Disneyland's Big Thunder Mountain (see the picture I took in link below)
http://en.wikipedia.org/wiki/File:RedRockUtah.jpg
http://www.utah.com/byways/highway_12.htm
http://scenicbyway12.com/
From California, stop for the night and get a cheap room in Las Vegas (Imperial Palace mid week $35).
Visit the Hoover Dam and take the tour. It's right outside Las Vegas.
http://www.usbr.gov/lc/hooverdam/service/DamTour.html
Get an early morning (dawn) start from Las Vegas, head north on I-15 to St. George, UT and turn off there for Zion and Bryce. You'll be at Zion by 11 AM and spend a couple of hours touring the canyons of the park. Then head to Bryce. You can make Ruby's Inn by sundown. If you time it right you can see sundown on the Hoodos (very impressive)
http://www.desertusa.com/mag03/feb/hoodo.html
Spend the next day or half day in Bryce and head east. You can then take the Route 12 Scenic Byway and head east toward Arches National Park. From there you can head to Colorado.
http://www.nps.gov/ARCH/index.htm
I really want to stress the beauty of Bryce and the Route 12 Scenic Byway. It's one of the most impressive drives I've ever been on.
BTW if you plan to go to more than one National Park, buy the annual pass. It allows a vehicle and it's occupants unlimited access to all National Parks for a year.
http://www.nps.gov/fees_passes.htm
Avoid what's left of Route 66. It's not what you think.