In addition to being a short walk from the old town of Eisenach, as mentioned above, Hotel Eisenacher Hof is directly below the Wartburg Castle (although this is a long, steep walk for those who go on foot). I don't believe that the hotel building is as old as some of its historic surroundings but it blends in perfectly. They stage a Luther-themed dinner show but I didn't see it to comment.
A con about one of the pros - internet access was free but was not functioning during my stay.