To get to Lisburn and Castlereagh, you can either drive or take the train. If you are driving from Belfast, take the M1 South and follow the signs for Lisburn. Alternatively, you can take the train from Belfast Central Station to Lisburn Station or Belfast Lanyon Place Station to Hilden Station.
If you are coming from Dublin, take the M1 North until you reach the A1. Follow the A1 North until you reach Lisburn. Alternatively, you can take the train from Dublin Connolly Station to Lisburn Station.
If you are in the nearby city of Newry, take the A1 North until you reach Lisburn. If you are in the town of Antrim, take either the M2 or A26 South until you reach the A1. Follow the A1 South until you reach Lisburn.
Overall, driving will likely be faster and more convenient, but taking the train is a good option if you prefer not to drive or want to avoid traffic.