Finding a place to stay isn't too hard - every city has hostels and motels that are comparatively inexpensive and usually have room.
Boston, New York and Toronto are awesome cities, I'd agree with mrspax though that the car will be next to useless in New York especially. If you're flying into Boston, then going to New York, then Toronto remember that it's a good twelve hours on a train or 8/9 hours driving from NY to Toronto. or vice versa.
Denver is pretty far out of your way, it's almost exactly 1,000 miles away from Chicago, so expect a good amount of driving time.
Car rental is not too bad from my experience - most of the travellers I met had rented cars and airport pick ups arranged, some of them were very nice. As it is though, just make sure you get one that's a decent size. I met five poor bastards who were travelling the country in a car no bigger than a Renault Clio.