The Upper Cloquet River north of Duluth fits your description perfectly.  The run is about 35-40 miles from Indian Lake to Island Lake and you won't hit a single bridge crossing (except a snowmobile trail), won't see a single house or cabin except at Alden Lake, will have the opportunity to canoe or portage 6-7 rapids of class I-III nature, will likely experience good fishing, probably won't see a single other paddler, and can camp at a number of DNR maintained campsites.  The river is an absolute gem.  The only problem is it is done running for the year.  Generally early-May to mid-June is a good time to run it for a relaxing, carefree time with decent water levels.  It can be run in early spring as well, but you have to be prepared for more volume in the rapids, cold water and possible ice in Indian, Alden and Island Lakes.
The lower Cloquet is nearly as good as the upperCloser to the Twin Cities, the lower Kettle River to its confluence with the St. Croix is an option.  I have never paddled it, but have heard good things.

I'd "second" the Namekagon River suggestion although it can be heavily used by the YMCA camp in Hudson at times.  Awesome river trip though!