If you drive north out of San Francisco, you can find Lava Beds National Monument a little ways off the beaten path. It’s pretty deserted most of the time, which is silly because it’s the only cave system I’ve ever heard of outside of the 3rd world where you don’t need a guide and you can touch, explore, crawl into, and generally examine everything. There are no light fixtures, no cement paths, nothing; they’re pristine, exactly as they were found, and you just get to scramble through them with your trusty flashlight and dented bike helmet, getting covered in dirt and having a blast. It’s like being six years old again. This is perfectly OK and not environmentally damaging because the caves are lava tubes and are not particularly old; there are no ancient dripwater formations to destroy with your skin oils, and there never will be, because in a couple thousand years lava will cleanse them again. This is not the most spectacular cave system you will ever visit, but it is the most sheer fun you will ever have in a national park.
The Lava Beds has the added bonus of being relatively deserted most of the time. The popular national parks (especially Yellowstone, Yosemite, and the Grand Canyon) will be quite crowded in July.
You really need to see the redwoods- They’re a real wonder of the natural world and a spectacular experience. However, you don’t need to budget a whole lot of time here, because at some point, it’s just another tall tree. You can spend a week or two here, or just a day, depending on your feelings. Here’s a list of the various places you can see them; I can vouch for Jedidiah Smith, which is extremely pretty.
The Grand Canyon is extremely spectacular. It will be packed in July. Granted, it can handle that a little better than some parks, because it has a roadside-attraction kind of a feel (pull up in your car, snap some pictures, move on), but it’s still not deserted solitude, and some people will be disappointed.
I’ve never been to Yosemite. I’ve heard nothing but good things, with the exception that it’s packed with camera-wielding tourists in July.
Crater Lake is pretty darn impressive. There’s only one, maybe two days worth of stuff to do here, though, so don’t plan on spending a whole lot of time there.
Based on my experience, I’d recommend flying into San Francisco, driving north through Yosemite, some part of the Redwoods, the Lava Beds, Crater Lake, and the Oregon Coast (Oregon’s whole coast is publicly owned and quite pretty. It’s not a white-sand-warm-water paradise, but rather rocky, misty, and imposing. The whole of the coast is covered by Highway 101, a very pretty drive that hugs the coast tightly and just littered with cute little towns. Try Astoria.) and finally flying out of Portland, OR. That’s a very reasonable two-week journey, with plenty of time for, you know, honeymoon stuff.
If you try to hit Yosemite, the Grand Canyon, and Yellowstone in one two-week trip, you’re going to spend half of your time in the car driving. It’s unfortunate, but that’s not a realistic two-week trip.
I don’t know if two weeks is a time-off-work limit, or a money-imposed limit, but you can save a lot of money by camping in the national parks in their campgrounds. They’ve got hot showers and you camp right next to your car. The West Coast is not oppressively hot in the summer because it’s very dry; 90 and dry is really more tolerable than 75 and humid, and of course it cools off a lot at night. The campgrounds are all well-equipped with bear boxes for your food, so it’s very easy.
It’s also pretty remote, however, and if you also want to check out some urban areas, it’s not going to be convenient, although you can stay in some nice hotels in Jackson Hole.