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.