There are a number of spectacular beaches in Portrush, the West Bay, East Strand and White Rocks.
West Bay, Dhu Varren, is a very popular beach, so can get crowded. Both beach and water are really clean and safe. Here you can go swimming, surfing (watch out for the rocks at the bottom end of the beach!), watch the coming and going of the small boats, or make sand castles.
East Strand, Causeway Street, is another beach granted a European Blue Flag premier seaside award. There are strong currents around here. As for surfing, you can hire the equipment at the Troggs surf shop, 88 Main Street (028 70 825 476). There you can also get advice on what beach is best to go to.