I was thinking, youcan rent a car and traval aroud the CA by yourself. Due to you have 2~3 weeks so you can drive form L.A. (or San Diego) to S.F. by I1 fwy. It's aroud the Pacific Ocean and there are many beutiful sights you can take pics., I also decide this kind of trip before I go back to Taiwan.
On the other hand, I never been to Great Canyon, but my friends said it's amazing!