The harbour is a popular spot for lunch, where you might even catch a glimpse of the local pelicans strolling along the pedestrian area. There are various options for boat trips and boat hire here. A visit to the MOSAICS is really interesting, the entrance is between the harbour and parking area, allow one or two hours. Tomb of the Kings is also recommended. The Old Town has a charming indoor market, which is about a 10 minute drive up the hill from the harbour.
Turn right out of Aphrodite Hills and follow the signs to Kato Paphos. Turn right when you reach the Amathus Beach Hotel, and follow the sea along to the harbour area (Parking on right hand side). Googlemap link.