Once you've climbed the famous "199 Steps" you will be greeted with the combined spectacular views of St. Mary's Church (with its vast adjacent cemetery) and the ruin of Whitby Abbey, which reportedly inspired Bram Stoker to write Dracula. Also, you will be rewarded with spectacular views of Whitby and the open sea. Very much worth your while, I can tell ya*.
When I visited the weather was less than spectacular, with grey skies, occasional showers and a bit of fog - all of which only added to the majesty and gloomy atmosphere of the place. The Abbey grounds were unfortunately closed on the day (the opening times vary widely during the seasons, so investigate before you visit), but even then I got a good enough glimpse of the abbey - and of course St. Mary's Church was open and available to "inspection". But for me, it was the view that left the greatest impression.
If you're tired from the 199 Steps you might also drop in at the brewery tap of Whitby Brewery, which is opposite of the abbey grounds.