Hi Lyndale,
I just returned from a trip where we combined Vegas with some National Parks and loved it.
We flew London to Vegas and spent 3 nights there, I felt this was a perfect length of time as I felt that I'd seen most of what I'd wanted to and was ready to see some other sights (although you could probably while away a few extra days shopping!)
We hired a car and drove to the Grand Canyon (4.5 - 5 hours, stopping at Hoover Dam) where we stayed in a lodge on the South Rim for one night. I highly recommend this! Sunset and Sunrise at the Canyon were amazing. We then drove back to Vegas where we spent one more night (only as a stopping point on our way to the coast, as the drive from Vegas to LA was too far in one day)
We skipped LA as didn't feel we had enough time to do it justice, and drove straight to Santa Barbara, spending a night in this lovely, quiet seaside town. We then drove up Highway 1 to Big Sur. The views are amazing and there are a lot of stops on the way. We stayed 2 nights at a little lodge in Big Sur and walked amongst the Redwoods and on the beach, also went into Monterey to the Aquarium. We then drove up to San Fran. We had 10 days in all and felt we had a good mix of towns and nature!
I'm sure whatever you choose you will Enjoy!