rocky,
With transport your best bet might be to go inland to for, example the Brown Trout
http://www.browntroutinn.com/ It is many years since I was there but it's a safe bet for a good meal in a nice location I'd say.
In Portrush the Spinnaker is one place I've been and really liked
http://www.tripadvisor.co.uk/Restaurant_Review-g209952-d2207723-Reviews-The_Spinnaker-Portrush_County_Antrim_Northern_Ireland.html
Another place I know: The Harbour Bar and Ramore Restaurant in Portrush
http://www.ramorerestaurant.com/harbour-bar.htm
which I see is billing itself as N. Ireland's oldest pub
Portstewart is a nicer town, imho, but I don't personally know any decent restaurants there - there's the Anchor but I remember it mainly for a lock-in many years ago (!)
Shenanigans
http://www.tripadvisor.co.uk/Restaurant_Review-g209963-d1723197-Reviews-Shenanigans-Portstewart_County_Londonderry_Northern_Ireland.html
is very popular, but I've never actually been. Others may be able to recommend it personally.
Obviously there are lots of other places but it's a few years since I was there.
HTH a bit