The Mournes are the highest mountain range in Northern Ireland, a compact cluster of granite peaks immediately east of Newry. Slieve Donard, the highest at 850 metres, is less than half an hour's drive away through Hilltown or Rostrevor and can be done as a long day walk from Newcastle on the coast.
For shorter walks, the Silent Valley reservoir (a Belfast water-supply lake with formal gardens), the lower slopes above Rostrevor, and the Mourne Wall — a 35-kilometre granite wall that crosses fifteen peaks — are all good options. The weather changes fast; even in summer, take layers and a map.