On a cold, rainy morning in Sept, 2010 I hiked the 3km from Stonehaven to Dunnottar Castle. Public transport is available, but you are cheating yourself by not walking.
The path to Dunnottar cuts through fields and is well-maintained. As you get closer to the castle, it begins to hug the edge of a cliff overlooking the beach about 150 ft below. There is no real danger though it may cause a bit of anxiety if you're afraid of heights as I am.
The jagged silhouette of the castle gradually grows on the horizon. As you walk, try to imagine the castle in its day, smoke rising from the chimneys and farmers working the surrounding fields, or armies laying seige to its walls.
The path entering the castle dips into a deep ravine that protects the entrance. There are plenty of steps but the climb is steep. If you have difficulty getting around, you may want to research accessibility to the castle.
The walls of Dunnottar enclose what was a fully-functioning city. There is a brewery, bakery, black smith, stables, a chapel, and most other amenities the noble family and guests of the day might require. Sadly, most of the buildings are only shells but still offer gorgeous views and retain a lot of their romance.
Before visiting, it is worth learning a bit of the castle's history. If you're making your way along the east coast of Scotland, Dunnottar Castle is a must-see, especially if you walk from Stonehaven. It is an experience I'll never forget, that's for sure.