I hesitate to call this "off the beaten path" since there are many tourists and it is well-known castle in Alsace. However, since it is definitely out of town and way up on a mountain, I'm calling it off the beaten path.
There is a long and interesting history to the castle and arguments about how "authentic" the restoration may be. It is fascinating to visit; there are plenty of authentic things in and about the castle; you should see it if you are visiting Alsace and finally . . . the views from the castle are absolutely spectacular.
There is a shuttle bus from the train station in Selestat if you don't have a car. The bus is wheelchair accessible but the castle is definitely not. You can see the castle and visit some of the lower areas and certainly enjoy the views and there is handicapped parking just behind the castle. http://www.haut-koenigsbourg.fr/en/info/navette
There were enough people there with us that we had to park along the road up the mountain (D-159) and it's a hike up to the entrance. There are several small paths through the woods that are good shortcuts if it's not too wet. If there has been recent rain, it can be slippery. It's a nice walk through the woods and you don't have to dodge traffic so I recommend the paths when it's dry.
The chateau is open every day except January 1, May 1 and December 25; however, the shuttle only runs every day during tourist season. The rest of the year it is a weekend and holiday shuttle.
The Pavillon du Haut-Kœnigsbourg, a small restaurant, shop and bookshop, is open from April to October. We did not eat there so I can't recommend it but it was busy and people looked happy. It certainly would be convenient if one did not have a car.