We need some help with the tail end our our trip to Ireland in September; we fly in to Dublin and are on a guided tour that takes us throughout the Republic of Ireland and hits most of the key sites and ends back in Dublin. We thought of going up to Northern Ireland for 2-3 days and seeing Belfast, being sure to see the new Titanic exhibits and then over to Giant's Causeway. We would prefer not to drive and maybe take the train.  We would like recommendations on hotels, restaurants and other things to do. After Northern Ireland, we want to end our trip with a stay at Dromoland or Ashford Castle or similar castle that you might recommend, but again would need it accessible by train and taxi. We could then fly out of Dublin or Shannon or even Belfast if there is a recommended castle there.  Not sure of the best way to get from Northern Ireland over to the west coast of the republic.

thanks in advance