Idaho!

"The Trail of the Coeur d'Alenes bike path follows the Union Pacific Railroad right-of-way from Mullan, a mountain mining town near the Montana border, to Plummer, a town on the prairie near the Washington border. More than 71 miles of paved path takes you from high mountain splendor, through the historic Silver Valley, into the chain lakes region, along the shore of Lake Coeur d'Alene, over the Chatcolet Bridge to Heyburn State Park, and finally climbs to the Palouse prairie: an adventure for the entire family" http://friendsofcdatrails.org/CdA_Trail/index.html

This trail connects to the the Trail of the Hiawatha which is also amazing. There is plenty of opportunity for doing a multi-day ride.