In the southern part of the state. Farm country with alot of amish folks selling crafts, furniture. Bike east into the bluff country, a dual sport would be alot of fun riding along the river.
http://www.google.com/url?q=http://www.barnresort.com/&sa=U&ei=lTY-U9vUH42_sQSlhYGgBA&ved=0CB8QFjAA&usg=AFQjCNEZ6YOHPntqjklYJIojKA2G4DT75g West of Duluth try fishermans point, if you like listening the loons call in the evening. Alot of backroads to ride in this area and your not real far from the big lake.
http://www.google.com/url?q=http://www.fishermanspointmn.com/&sa=U&ei=3TY-U5yFJenEsATf9oEI&ved=0CCEQFjAB&usg=AFQjCNHL4h1Kc9Gsjtt6B152tU0xpg-qIw On the west side of the state, plenty of back roads to ride on and the old mine area to explore. very open farm country.
http://www.google.com/url?
http://www.google.com/url?q=http://www.lakeshorervpark.com/&sa=U&ei=nTM-U9bUJLPKsQTv7IDwCQ&ved=0CBsQFjAA&usg=AFQjCNEFqb3kdLnbnxlYAjyubaM38RhjAAAlot of state parks on the east side of the state, you will spend alot on entrance fees as they will want one on each vehicle. but lots of back roads along the St.Croix river.
I hope this helps and you have a great trip.