Playing into the Air Bud reference we made earlier, we figure you should try introducing your Great Golden Dane to the sport of basketball if you're looking for a less conventional way to bond with your pet. Dogs naturally won't be able to dribble or dunk the ball, but they can learn how to bounce it off of their snouts and into the basket if you practice with them enough.
This activity is the next best thing to going out and solving mysteries with your dog, a la Scooby Doo and the Mystery Inc. Gang. Great Golden Danes have great senses of smell (yet another trait they inherited from both of their parents,) and they can learn to find items and people that are well hidden with enough training.