If you're looking for isolation, Valley of the Gods in Utah is definitely the place to be. Not a structure in sight, and only a dirt road leading into it. Pretty spectacular. I'm not sure if you're allowed to camp or stay overnight - legally, that is - but I've been on a photo workshop where we did a sunset/moonrise shoot and it's still one of the best memories of my life. There's a spot in the valley where every sound you make reverberates exactly 7 times. A pretty mystical place all things considered, but a bit out of the way. If you make a trip to Monument Valley, it's only about an hour away.
Capitol Reef national park is where all the hot landscape photo action is these days, it's not all that well known but pretty spectacular regardless. It's not that far away from Zion, but on the way you should also check out Bryce Canyon, probably one of the most spectacular vistas I've ever seen. Even more otherworldly and outlandish than the Grand Canyon. Utah in of itself is amazingly beautiful all around that area.
Around California, Mono Lake is pretty interesting and certainly worth taking the time to do some sunset shoots in. On the way, there's the Ancient Bristlecone Pine Forest in the White Mountains. Not only do you get one of the best driving roads in the world on your way there (you will really want a sports car here but the last bit of the road is a rough dirt track IIRC) but you will also have some pretty awesome vistas once you arrive. Time your arrival with some cloud cover, and being at 11,000+ feet you're almost guaranteed to have some spectacular fog shots.
If you just want to get away from it all, Lake Powell in Arizona is pretty interesting, just leave your environmentalism at the door as it's a man-made lake and a real ecological disaster. Still, a very beautiful area. Rent a houseboat, moor anywhere you want along the lake, and do all the sunset shots you could ever wish for. Just watch out for storms on the lake, they can be pretty vicious. Not the cheapest getaway, but oh so very well worth it. Bring a toolkit; I've had both engines cut out in a houseboat in the middle of a storm, and was forced to fix both of them with a coathanger, a single bandaid, and two shoelaces, for lack of anything else. McGuyver was a wimp.
Sorry too drunk/lazy to provide links.
I do love Antelope Canyon, and I do have some shots from it that are actually not terrible. May post them later at some point. Also, Yosemite may have tourists all over it like flies on shit, but that's not to say that there aren't any really interesting, less well-known spots. A photo workshop in the park would be my recommendation.