I would hike Hermit Trail or Havasupai trail at the Grand Canyon. Spend a day or two hiking and relaxing at the bottom. You won't see too many other hikers on the Hermit trail once you get past the first 2 miles. If you have a tent, you can stay in the national forest outside of the park for free if you know how to rough it.
http://www.sfgate.com/cgi-bin/articl...RGTBH8UAO1.DTL
Part of me says that a good route would be from Chicago to LA on old route 66/I-40. You could hang out in Chicago(Others may be better suited to tell you want to do, I can only say to go see The Second City show)
You would head down through the midwest and end up in New Mexico, Arizona, Nevada and California. Make sure you drive during the day when you are in Arizona/Nevada, it is really neat.
In Canada, I would recommend staying a night or two at tthe Banff YHA youth hostel (preferably Friday night, you will meet a lot of people there on that night). It is the best one I have been to in the world (well at least in Canada, New Zealand and Australia). Also drive during the day through the Banff national park (on 1) because once you hit 30 miles outside of Calgary, it is flat and plain for a long time.
How many months are you going to do this in? Take your time and don't rush things. And don't spend all your time getting someplace if the trip isn't fun.
If you haven't seen the movie Into The Wild, I would recommend watching it.