Go behind the throne in the main room and go to your private chambers, in front of the fire place next to your bed is a sheet of paper on a table. You need to pick this up and fulfill part of the main quest line. After you do this go into your inventory screen and then to your quest items. Select the Dragon Stone and a submenu will open up. You will be able to select to leave the tower with the option on the far right. Or you can use the waypoint shrine located in your private chamebers too.
