Marselisborg Gardens
Just south of the city is Marselisborg Palace, the summer residence of the royal family. The changing of the guard takes place daily at noon when the king is here. When the royal family is away (generally in winter and spring), the grounds, including a sumptuous rose garden, are open to the public. It's worth checking out Marselisborg Beach and especially the Infinite Bridge, a circular bridge floating over the water during the summer (in winter, it's taken down), while in the area. You can get here on several buses from the city center.