where in CA are you starting? i suggest you start on the I-40...Grand Canyon is off that freeway. and the 40 goes all the way to the east coast.
I agree. If you are going to the Grand Canyon, I-10 is WAY out of the way. I-10 takes you through Phoenix, which is roughly 5 - 6 hours south of the Grand Canyon. You can do it, but you'll hae to go up I-17 through Sedona to get there.. not that it's a bad thing, but it's become heavily commercialized as of late.
If you're starting in CA, Here's what I would suggest.
Start in Santa Monica. Take the old Route 66 out of the LA Basin, and follow it as much as you can along I-40. It should drop you off about 20 miles south of it by the time you hit Needles, CA. Then take US-95 north until you catch it again going through Oatman, AZ.
http://en.wikipedia.org/wiki/U.S._Route_66
http://en.wikipedia.org/wiki/U.S._Route_66_in_California
http://en.wikipedia.org/wiki/Arizona_State_Route_66
http://en.wikipedia.org/wiki/Oatman,_Arizona
You'll like it there; really nice kept-away tourist trap. Mind the donkeys: they run the town (no joke). Follow Route 66 there all the way through to Kingman, which you'll pass a classic 1950s/1960s gas station. (Side note: Kingman is only 100 miles south of Las Vegas). There's more of the classic buildings in AZ, as 40 follows 66 through Seligman, Williams, Flagstaff, and Gallup, NM. Williams and Flagstaff put you about 2 hours south of Grand Canyon.
From there you can stay on 40 through to Albuquerque and take a short trip up through Santa Fe and back. Here, you'd have a choice: I-25 south to El Paso and pick up I-10 to take it across the belly of Texas, or stay on I-40 to Amarillo, then take US 287 to Dallas to I-45 south. Either route lands you in Houston, which puts you at another beach/college town. From there, I-10 through New Orleans, Biloxi, Mobile, and on to Florida.
BL.