Do it!
Yes, Easyjet flies into Belfast International Airport.
You can either hire a car there (unfortunately not by Easyjet) and travel from the airport to the coast without any problems.
Or you can get the Airbus from the airport to the main bus stations and railway stations every half hour or so. If there are a few of you it works out the same price to get a taxi.
The Giants Causeway is a lovely place to visit, and I have been too afraid to even see the Carrick a rede rope bridge!!
Portrush is a true seaside resort - funfairs, etc and a night life. Some of the university students from University of Ulster (Coleraine Campus) live there. Coleraine is the main shopping town in that area, and you could always see if you could visit the Bushmills Distillery - the oldest legal distillery in the world.
Here are a few links to try...
http://kingdomsofdown.com/
http://www.guide-to-nireland.com/visguide.htm
http://www.discovernorthernireland.com/
Let me know if you want any more info.
