Royal County Down was laid out in 1889 by Old Tom Morris on the dunes at the north end of Newcastle, with the Mournes as a backdrop. It has two 18-hole courses, the Championship and the Annesley Links. It hosted the Walker Cup in 2007 and the Irish Open in 2015, and Tiger Woods is said to count it among his favourites.
Even if you don't play, the beach in front of the links is the start of the walk north to the dunes of Murlough.