My family has a cabin 3 miles northeast of Indian Lake.  It is a beautiful area and that river is usually not very busy.  Indian Lake has a nice state forest campground where you could stay the night before your trip.  I would definately check into river levels however, as they can be very low in spots, unless you are one of those odd people that enjoy dragging your canoe over rocks and mud!

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!

Take a trip to Hayward, WI and paddle the Namekagon River.  You do get the occasional road noise in stretches since the river flows so closely to Highway 63, but it also flows away into wilderness-like areas where you'd think you were the only people for miles.  The river flows right along, but there are no true "rapids".  Just plenty of riffles that are fun enough.

Many campsites along the river - and they're free.  They are, however, first come, first served.  Go during the week if you can and you'll have no problem at all finding an open site.

Remember to Leave No Trace.

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.

Im looking for a cool stretch of river to canoe.  Preferably about 3 hrs or less from the twin cities.  Im looking for nature with few houses, some conoeable rapids and a nice campsite to accomadate about 5 people.  Any suggestions?