I went on trips like that as a kid, led them as a young adult, and about five years ago took my nephews, 11 and 14, on a weeklong bike trip in Nova Scotia. Those trips stand out in my memory as highlights of my youth. Most kids love the independence, self-reliance, and adventure. Even when it's cold and wet and miserable, the next day you look back and say "I did it!"
Selling the trip in advance is key -- involve the kid in route selection, gear selection, preparation. Most kids love that kind of stuff. The more excited they are the more positive they will be. Have goals along the way, things to see and do. Showing pictures of where you're going is very effective for generating interest. Some kids will turn negative and get difficult, which is no fun for anyone. Have a contingency plan that is more than packing up and going home if that happens.
The biggest wild-card is the parent/child relationship. Since I've become a parent I've learned that children behave differently toward their parents than toward anyone else in the world. You have to look at the particulars of your own relationship.
Get the kid excited, and go! You will create memories you'll both treasure for a lifetime.