In reply to ERU:
A bit more info...for internal flights (esp. if you're not going cross-continent & sticking to the western third), stick to Southwest alone (all others will charge you for checked bags). You still get to check 2x 50lb bags per person "for free" and it's trivial to change flight times (you just don't show up & they hold the value of your ticket for up to a year & you can use it anytime). Go with a light tent & a small rental car - much more convenient and cheaper than a camper. You can always get a cheap motel once in a while to shower (Motel 6 chain for example). I'd recommend a few locales for August:
Wind River Range in Wyoming - count on a day of approach & having to set up a backcountry camp. More specifically, go to the Cirque Of Towers. No permit issues, many long routes on granite spires.
Tetons in Wyoming - climbed very little there but it looks good. It's a national park meaning you have to worry about securing backcountry permits (quotas) if you're going overnight.
Devils Tower - it'll be HOT in August but if you can suck it up, try to do a route on it since it's so unique (no approach, no permits).
Rocky Mtn. National Park in Colorado - check out the Diamond on Longs Peak for example. Same issue - national park = backcountry permit issues.
High Sierras in California - again, count on a day of approach & backcountry camping for most objectives. Except for stuff in Tuolumne (which for the most part has short approaches), it's not a national park but you need to get a backcountry permit and some destinations are VERY popular (& quotas are stingy).
Lovers LEap is good - zero approach, mid-sized routes & no permit issues.
If you're going up to Squamish & happen to be driving, you should make a stop in Washington state. One area that comes to mind is Washington Pass. Short approaches, long climbing routes (granite), no permit issues and a very alpine ambiance. And it's not as rainy as say Squamish. Another spectacular (backcountry) area in WAshington (also plagued by permit issues) is Alpine Lakes Wilderness by the town of Leavenworth (look up Prussik Peak, Colchuck Balanced Rock, Dragontail peak etc.)
I'd check out all these areas on mountainproject & plan a route. If you plan well, you won't even have to fly - most of these can be connected with a single day of driving (long day in some cases). I bring up permits since these will tend to slow down your progress if you have to wait out a day or two to get one. I'd forget UT, NV, AZ this time of year - the high country stuff you might be able to eke out there seems relatively lame.
PS public transport?? what's that?
Post edited at 18:32