Following on from the geocaching link, there is a geocache hidden in Redburn Country Park in Holywood. I was there for a dander with Rebecca and her sister a few weeks ago. Rebecca's sister seems to know a lot about local history. Apparently Redburn was owned by the Dunville family, who used to own the world's biggest whiskey distillery, which was based in Belfast. They had a menagerie in the grounds of their house, and you can still see the bear pit, as you walk up towards the top of the park. The lady of the house was an adventurer and pioneer aviator and balloonist.
There is a great view from the top across the Harbour Estate to the Lough, and you can watch the planes coming and going into Belfast City Airport.