Great Danes puppies have spurts of activity but you shouldn't do heavy exercise with them until their growth plates close or you can really injure them. This could be 1-2 years. Heavy exercise would include jogging/running on pavement. Adult danes can range from couch potatoes to super high energy dogs who compete in agility.
That said, walking/hiking can be done with a younger dane as long as you condition them slowly and are careful with the terrain. I used to hike all the time with my dane, he could do around 6 miles comfortably by the time we was 1.5 years old. Lots of danes love to play with other dogs, I often took my dane to the dog park for an hour or two at time to let him run around.
If you know you want an active dane puppy, you really need to go to a reputable breeder who has health tested stock to ensure they can handle the exercise. They can also match you with a higher energy pup. You could also rescue an adult who's health status and energy needs are already know.
