This scenic and tranquil park is located on the outskirts of Limavady and offers spectacular riverside views and woodland walks along with opportunities for salmon and trout fishing, canoeing, rock climbing and orienteering. BONUS: It also has a cute coffee shop with good food!
Portrush is an awesome tourist town with spectacular beaches, restaurants, and small amusement parks (more like a carnival for anyone from America). It can also be the starting destination to bus/cycle/drive the Causeway coastal route on which you will see Dunluce Castle, the Giants Causeway, the Carrick-a-rede rope bridge, and Rathlin island.
Dunluce Castle is one of the most incredible castle ruins in Ireland. You can (for a small fee) even walk throughout the inside the castle, and learn its history. If you're interested in cycling some of the majestic coastal cycle routes, bikes can be rented in Portrush.
The Giants Causeway is one of Northern Ireland's gems and is easily accessible via bike/car/bus. The cliffs and fabulously-shaped geometric rock formations were crafted by Finn mac Cumhaill (a hero of ancient Ireland; he it was who also formed the enormous nearby depression in the land south and a little east of the Causeway—which, when it eventually filled with rainwater, became Lough Neagh—by lifting a large sod of earth to hurl at a rival in Scotland; he missed, but in the process created the Isle of Man) and constitute the remains of the bridge that he built from Ireland's north coast to Scotland. Some also claim that the formations are the result of volcanic activity a while back.
The Rope Bridge is another beautiful site on the Coastal route, at the end of the cliff side walk. The old bridge leads to a small island off the coast that glimpses stunning views of the Giant's Causeway and Rathlin island. On a good day, you can spot dolphins jumping out of the water. This spot can be easily reached by bus/car/bike trails along the coast.
If you're looking for a day out on the ferry to see some beautiful castles, lighthouses, and cliffs, the Raithlin Island is just the place. The Island can be accessed by ferry from the coastal town of Ballycastle.