OK, so my girlfriend and I want to roadtrip this summer, never done it before but I've driven 200+ miles in a day multiple times, and I've done NYC to north of Montreal straight, so I'm not real worried about the driving. We don't want to plan the activities, but the basic things we'd like to do:
1) Drive as much of the old rt 66 as possible, ideally from the chicago area to LA pretty much, drive this on the way there.
2) Drive from LA up to the Bay area, we have friends there.
3) Drive from the Bay area to the denver area (family), possibly going through Las Vegas, but that's not imperative
4) From Denver, start heading back to NYC
5) We only have two sites we want to see as of now, the Grand Canyon and Yosemite, other than that we're content just seeing what there is to see on the road/along the way.

Is 3-4 weeks enough to do this? How feasible is it to do minimalist hotel/motel room stays (primarily to save money, any night we can avoid paying $40 to sleep and save a couple hundred overall would be wonderful), instead just trying to find truck stops/hospital parking lots to sleep in? Thanks for all your help, sorry if this is a post some of you have seen the likes of 100 times :)