I'm from belfast (just outside it), and if I was visiting here I would come in May, June July or Aug, as this is when we have a bit of sunshine. I recommend a b&b, maybe outside belfast, as youy can travel in by bus or train etc. Giants causeway is around 60miles away, you can drive up and it's quite straight roads, well sign-posted. It's a nice day trip. You could also go to portrush or portstewart for a few days, as there are nice beaches. They are close to bushmills and G.causeway.
When are you thinking of coming over?
If you need any more help or advice just pm me x