Ballycastle hosts each year the Lammas Fair, where music, stalls and general good times may be had. It is around 25 minutes from Portstewart and would be a great stop for those planning on doing the Glens of Antrim drive.
Grand cliffs that can be seen from the town, and can be explored on foot after driving up windy (in both senses) roads. Caution is recommended, however, as the drops are steep and the side unbarricaded.
There are a host of coffee shops, pubs and restaurants - and a great fish and chip shop near the harbour. Ballycastle is also the point from which you can reach Rathlin Island via foot and/or car ferry (cars cannot be taken for day trips, or even for less than around a week - please check before, if your plan is to bring a car).
But once on the island you'll soon realise you don't need a car if you like walking, which is what attracts visitors to the island. It is a puffin sanctuary (at certain times of year) and there are often buses laid on for those who want to reach it quickly (it is at the farthest point on the island from the harbour).