Trailbadger as mentioned before. They used to run DH races in Coolaveely (sp?) forest near Ballycastle. Binevenagh (aka Ballycarton) between Castlerock and Limavady is fairly close, and has a stunning trail off Binevenagh lake down into Ballycarton forest. Further south, Garvagh has some trails in the forest there, Belfast has Cavehill (scene of the recent Red bull Foxhunt event) and Belvoir forest (Belvoir is pretty boggy).
The mournes have the best riding, Tollymore and Donard near Newcastle, Castlewellan for some xc stuff, and Rostrevor for a good day in the hills. Bigwood is great, however it is private land but that doesn’t stop anyone, just be careful if they are shooting in there. Post on MTBrider and get a local guide, the best way to find the best places.