Giant's Causeway

Was there in mid October 2010 and the weather was fine. A little cool and overcast, but a light jacket took care of that. By the end of that day it cleared upend was sunny. We had a rental car and stopped at Carrick-a-rede bridge, Giant’s causeway, Old Bushmills distillery, and Dunluce castle in the same day. We spent the night in Portrush.

I have been there in Oct, yes, yr Choice of head gear, perhaps light gloves. Also realize some stones are worn smooth by decades of exposure and could be damp, so choose good shoes. You don't necessarily need hiking boots, but choose something with good tread that will also keep yr feet warm for the whole trip.

I took the train from Belfast to Coleraine and then the bus on from there. It worked very well.
Dublin, You would take the train (or a bus if you prefer) from Dublin to Belfast. Switch trains onto Coleraine/Port Rush.