The Boundary Waters Canoe Area in Minnesota registers as one of the quietest places on the planet:

what he calls the last great quiet places, areas that clock in at audible human noise-free intervals of 15 minutes or more. He only counts areas of around 3,100 square kilometres (1,200 square miles) or larger – enough to create a sound buffer around a central point of absolute quiet. Over the years, his list has shrunk as he returns to a previously quiet spot, only to find it now polluted by noise. Still, he says 12 such quiet places exist in the US, with more found around the world.

A spot in the Hoh Rainforest in Washington is one, as are places in Grasslands National Park in Canada, Boundary Waters Canoe Area in Minnesota and Haleakala National Park in Hawaii (see gallery). The others, however, he keeps confidential.

source: http://www.bbc.com/future/story/20140117-earths-last-place-w...

I've been to the BWCA several times and it's incredibly serene and peaceful.

...You'll hear only the constant drone of mosquitoes and your own screams as they slowly devour you...

Seriously, though, it is a fantastic place. Quetico (the Canadian side) is even more remote and beautiful, i.m.o.