go hike a portion of the great continental divide. like through yellowstone. the entire continental divide takes 6 months. i was watching this show on pbs though with this amateur film maker who recorded his journey and a few others. it looks really epic. im kinda ticked i started watching it in wyoming as he traveled north. but the scenery was epic. and there is definitely some cool shit you walk through (abandoned mining towns, tons of shit you never see in yellowstone from your car window, walk through the same paths lewis & clark did).
car trips sound cool, but faace it your stuck on an interstate, staying at cheap motels, and you gotta plan things to do which requires getting off the beaten path.
you could take a train out of chicago to seattle which takes about a day and a half. see a bit of the country that way, then drive from seattle to LA in a rental checking out sequoia national park, the golden gate bridge, mt hood skiing, whatever. but you would have to plan or else you will spend all day dickin around in your car getting no where closer to your eventual target (say a flight that is 2 weeks out from LA to CHI)
or you could walk the Appalachian trail, a portion of it rather. Up in NY, then go to NYC....
