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Napa could easily be fit into your trip, probably working best right before San Francisco. There are also wineries along the central coast between SF and LA.

Utah is filled with great things to see and do, and it is always "worth it," but the question really is at what cost? In this case, the cost is time, and you'd have to decide if you're willing to give up time at other places. Right now, you don't have a lot of extra time, and shortening your city stays really is your only option, unless you can extend your trip.

The West Rim really is not the Grand Canyon. The canyon there is only about half as deep as it is within the National Park, visiting the Indian Reservation there is also very expensive. It just doesn't really compare to the actual Grand Canyon. If I were you, I would make actually visiting the Canyon a top priority, if that means shortening your city stays by a day or two, or using the extra time you think you'll have.

If you do go to the National Park, You'd want to go there directly from Los Angeles, you can get there in one full day on the road. After Grand Canyon, then you'd go to Vegas. If you were interested in adding some stops in Utah, you'd most likely do them after Grand Canyon but before Las Vegas. The exact routing, of course, would depend upon which stops you end up adding.