I think some background is in order so you know my perspective.

I spent 3 summer months traveling to the western continental US in 2000. I've been to every state west of the Mississippi. Since 2000, I've lived in Arizona and traveled extensively in Arizona, New Mexico and California. I enjoy hiking, skiing, mountain biking and visiting big cities and national parks.

I'd recommend staying in extended stay hotels and getting as much travel in as possible over picking up apartments.

Let's assume you find your way to Jackson WY. A cool small town in NW Wyoming. I'd visit Grand Teton and Yellowstone NP then head through Missoula, Montana to Coeur D'Alene / Spokane. Then head toward Seattle (or possibly the Columbia River valley to Portland). This is probably a week or two if you are working on and off.

I'd recommend Vancouver and Seattle as a base for the next week or two. I'd goto Victoria from Vancouver. I'd head to Olympic NP and Mt Rainier from Seattle. Mixing off days in downtown Seattle and/or Vancouver.

I'd head south to Portland and set up base here for another week or two. I'd hit up Mt Hood for some skiing in late summer (just fun because you can). And I'd cruise the Oregon coast. There are a ton of really cool cities on the coast. Portland has great breweries that should not be missed.

Next I'd head south toward San Francisco. Consider visiting Redwood NP. It's quite an excursion. If you do you'll probably want to take the 101 south. Even though this is a scenic drive it can be a bit crazy after six or eight hours of driving crazy coastal roads. If you are into easy going hippy / wine culture then this is a must. Since you'll pass through Eureka, Sonoma, Santa Rosa, Napa, etc.

I've only visited San Fransisco and San Jose a few times. This is a good place to set up a base. I'm assuming there will already be plenty of advice on visiting this area. There are definitely plenty of tourist areas that can be taken in depending on your interests. Yosemite NP and Lake Tahoe and Napa are a must if you are in the San Fransisco area.

I've driven from San Fransisco to LA a number of times and prefer the mountain drive. Versus the coast drive. Both are superior to just taking the 5.

The mountains: Yosemite and Kings Canyon and Sequoia NP. Farm land in between mountains. Definitely worth seeing the "rest" of California. Also great if you love the mountains and forest to the coast.

The coast: Monterey, Pebble Beach, San Luis Obispo. Golf courses, wineries and marinas. Definitely good if you have a significant other and a lot of cash. If you can afford it and aren't into mountains and giant trees this is the way to go.

Other than the beach cities I'd skip most of LA. With the exception of specific things you are interested in. Still you'll have to drive EVERYWHERE and it's huge. Maybe hook up with a friend there and get the tour that way.

Set up base in San Diego and Long Beach. The area is really cool. I've only visited as a tourist but it's definitely a lot of fun. You'll get the socal feel without having to spend too much time in LA.

I'm a big rock climber so I'd recommend Joshua Tree NP on the way out of California. But if you insist on some gambling then go through the Mojave / Death Valley to Las Vegas. I'd spend less time in LV and hit up a nicer hotel while there. That is just me personally. If you are in LV in the middle of the summer you should shop for deals beforehand because you'll be able to get some insane room rates. I've stayed in a huge 1200 sq ft suite for 150 a night in July and August. Always ask when you check in if there are any available upgrades.

Then I'd head to Zion NP, Bryce NP and end in the Grand Canyon NP. You could loop as far out as Moab and back to the Grand Canyon. I don't know how best to visit this area with a single base. This is all time dependent. I would recommend doing the south west late because Monsoons will have arrived. It will be somewhere between insanely hot and pleasant. But in May-July you'll just end up with the insanely hot bit. Seeing the monsoons tear across the SW is really awesome too. So with some lucky you'll catch some impressive storms.

If you have time and are down with the desert I would hit Tucson. Saguaros can not be found anywhere else in the world (just southern AZ and nothern MX). It's a laid back and cool town and where I currently live. It's one of those "big" small towns.

From there head to Santa Fe and on to Denver. If you are a bit insane and have the time I'd head through Durango and take the 550 up and around through the Rockies. If you are in a rush take 25 all the way through. The Great Sand Dunes NP is bizarre and just off of 25. It's a good place to stop if you have time and weather dependent. I personally prefer the ski areas on the western side of the Rockies. The cities and ski areas have a lot more character.

Have a great trip!