The beaches around Ayia Napa are some of the best in the Mediterranean -- white or golden sand, shallow turquoise water, and most hold EU Blue Flag status. Nissi Beach is the most famous and liveliest, with water sports and music all day in summer. Makronissos is a good alternative with more space, and Harbour Beach near the centre is calmer and better suited for families.
For something quieter, head east toward Cape Greco. Konnos Bay is a sheltered cove with clear water and fewer crowds, and the coastline between Ayia Napa and the cape is full of rocky inlets and sea caves worth exploring on foot or by kayak. Ayia Thekla, west of town, stays relatively uncrowded even in high season.