Get active, choosing from amongst snorkelling, diving, swimming, paddling, paragliding, whizzing around in a banana boat and boat-trips with the opportunity to snorkel. They're mainly available in the more heavily built up resorts.
Head off the beaten track, but sure you know what the tides and currents are doing as often there are no flag systems or lifeguards. Coral Bay in Paphos is calm and child friendly, with a lovely harbour with coloured fishing boats, boat-trips and a fun covered market. Then bribe the kids with ice creams to walk up to Paphos Castle, with brilliant views. A short walk from the harbour you’ll see ancient mosaics (the site at Kato) from Roman times.
Soak up the atmosphere at the mysterious Tombs of the Kings and the catacombs at Agia Solomoni – fun if somewhat gloomy. This is where persecuted Christians hid.
Head for Phinikoudes Beach, one of Cyprus’s most famous, with plenty of cafés and bars. In June it hosts the two-week Larnaca Kataklysmos (Flood) Fair of folklore, with craft and food stalls and outdoor performances.
Take a trip up to the Troodos Mountains, where you’ll find surprisingly green and forested land and Kykkos, Cyprus’s main monastery.
Explore Lefkosia, the largest town in Cyprus, with enough historical sites and museums to fill a day, plus good shopping.
In the east of the island, visit Curium, with the best amphitheatre on the island – the Magic Dancing Waters Live Show will amaze younger kids.
Head for the camel park at Mazotos, just outside Larnaca, or the donkey sanctuary just outside Limassol.
Go roaming in search of beautiful and interesting inland villages that will show you a bit of the real Cyprus – once there, have a wander then sit in the shade of a veranda to watch the world, and your children, go by.
And make sure you visit the Baths of Aphrodite, a pretty spot where the goddess used to take to the waters.
Other possibilities for half-day outings are little Pafos Zoo (now incorporating Pafos Bird Park) and Aphrodite Waterpark, with plenty of rides and pleasant landscaped gardens to walk around.