Cyprus' most famous beaches are all in the south of the island around the town of Agia Napa. The most well-known is Nissi Beach, a long stretch of perfectly white sand with an island rock outcrop just offshore that's on the western side of Agia Napa town. Be aware that Nissi's beauty means that it can get heavily crowded in summer.
If you're trying to escape the crowds, head to Kermia Beach (two kilometers east of Agia Napa), which is smaller but just as pretty, or head to Konnos Beach (two kilometers east of Kermia Beach), which is a great choice for families with kids who want to get into the water as the sea here is calmer than elsewhere.