Castlewellan Forest Park
Enjoy a walk around Castlewellan Lake and Arboretum in County Down. The park contains the national Arboretum of Northern Ireland with a variety of interesting specimens from all over the world. There is also a peace maze and the the Scottish baronial Castlewellan castle. It's a lovely place, with views towards the Mourne Mountains and surrounding countryside to enjoy. The park is also great for mountain biking with green, blue and red grade trails to try.
To extend your exercise, just head to the south and visit the lovely Tollymore Forest Park. The expansive 1600 acre park contains an arboretum, the Shimna River and two forested hills known as the Drinns.
Also nearby is the splendid Murlough Bay National Nature Reserve where there is a beautiful sand dune system, woodland trails and a wonderful beach.