You might think from photographs you've seen that Neuschwanstein is the highest thing for miles around, and you would be wrong.  It is actually situated atop a medium-sized hill and completely surrounded by much taller mountains. 

Part of the 'grounds' includes a footbridge, the Marienbrücke, 'Marie's Bridge', across a chasm to one of those other mountains.  From the Marienbrücke you have an unobstructed view of Neuschwanstein from turret-height.