That is a big undertaking
Bob,
Three months to explore the lower 48 sounds like heaven to most of us. It is a reasonable span of time to see much of the country -- it sounds like your and your daughter are experienced travelers. The first suggestion I would make is to check out the various sites we have listed on the <a href = "http://www.roadtripamerica.com/links/travelogs.htm">Journals<a/> page -- several of them document other cross country adventures and they will provide ample intel for planning your trip.
Mark
Well, I like urban driving
If you are fine with Chicago, then in my experience, there is no city that will bother you. Even Manhattan is easier to navigate than Chicago at rush hour. Parking rates are a little extreme in Manhattan, but those other cities are reasonably on par with Chicago.
Mark