A few miles on the east coast outside old Rhodes Town, you come to Kallithea, once a 1920s Italian spa town, with mock Moorish buildings and sheltered coves, now a long string of hotels and resorts.

Aldemar Paradise Village is the latest - a vast complex set among palm trees and pines overlooking an impossibly blue sea. This is a child's paradise, so it comes complete with water slide (brilliant), Captain Pugwash pirate ship (wow, is that real?), and a forest of straw sun umbrellas, dotted along the coast like conical hats (sweet).

More town than village, paths lined with boxes of petunias wind down from the main hotel and apartments towards the beach. But there is no scent of flowers or sea - the unmistakable odour is that of sun oil from row upon row of bodies cooking on racks of sunloungers.

This is what Rhodes is best at. Forget any romantic notion of tiny fishing villages amid ancient Greek ruins. Forget also any preconceptions about tacky Faliraki nightclubs. Most of the island is given over to relaxing family tours, with cheap flights thrown in. Such is the demand that tiny Rhodes airport is building a new terminal to double its capacity.

So which pool to chose? The children decided by leaping into the first one they came to and then refusing to move for the next eight hours. The first day, the height of our adventures was a swim under the miniature wooden bridge spanning the junction between one pool and another, and vague thoughts about joining the aqua-cise class that had chosen La Bamba as its theme tune.

We had a mountain of deliciously trashy holiday reading planned for the free hours during children's club.

The food went down a storm. A self-service buffet with dozens of dishes was laid on in a vast dining room each night. What it lacked in charm was made up for in staggering efficiency. Over 500 people passed through every evening, zooming in on hot plates of Greek, Italian, German and English food.

We intended to try a different pool the next day but didn't quite make it. It was day three before we made it the 500 metres down from the terrace to the Paradise beach to try the snorkelling. And that was only because of the umbrella wars. To bag one by the pool, you had to be up early.

Nothing for it but the beach. Snorkelling over tiny iridescent fish right by the shore was a big hit, as was the banana boat - an inflatable dragged by a speed boat across its wake so that you bump and crash through the surf in a water version of a roller coaster ride.

But by day four my husband and I had cracked and decided that perhaps it was time to explore the outside world. We hired a car and set off in the scorching heat for the hills. Within 15 minutes we were back in old Greece, on winding tracks through olive groves among quiet villages and parched rock. We had Sunday lunch in the pretty village of Psinthos, on the road across the central mountain spine of the island.

Here Greek families (but few tourists) come to the restaurant by the Fasouli springs, where under the shade of spreading plane trees, tables are set by the ford over the stream. You help yourself to jugs of water from the springs and are invited into the kitchen to see the dishes of the day - roast goat stuffed with rice, butter beans slowly baked in tomato sauce, steamed bitter greens, all served with local wine. After lunch, we wandered up the brook, and as we disturbed the silence, crowds of dazzling red-and-black butterflies rose up from the bushes ahead.

In the evening we ended up at Lindos, further down the east coast, with its spectacular acropolis perched on a fortified rock overlooking the sea, and its tumble of picturesque white 17th century houses below. The guidebooks all advise avoiding the town between 10am and 4pm in peak season when swarms of coaches disgorge tourists into the steep streets. Every inch is given over to shops selling tat and restaurants dishing up factory Greek food, but even so they cannot quite manage to spoil the extraordinary beauty of the place.

The other cultural gem within easy reach of Kallithea is Rhodes Town itself. Its medieval walls and cobbled streets, full of fine honey-coloured stone buildings, are perfectly preserved. You can meander along narrow alleys where ancient houses are propped up on flying buttresses into grand squares with cooling fountains.

It is small enough to allow yourself to get completely lost in its different quarters until you find yourself back at the avenue of the Knights of St John and its line of austere 16th-century inns.

We made two brief excursions in the evening to satisfy the adults, but by now the children were addicted to pool life. Our eldest had formed a gang of friends and dedicated hours to going down the water slide in a chain; the middle sister had attracted an older Italian boy who enjoyed thrashing her at giant outdoor chess; and the little one had learned to swim 10 metres without drowning.

Way to go

The package holiday: Planet Holidays (0870 066 0909, planet-holidays.net) can organise a week's stay at the four-star Aldemar Paradise Royal Mare hotel (+210 62 36 150, aldemarhotels.com) on a half-board basis for £589 per adult and £309 for one child sharing in May including flights from Gatwick. This rises to £655/£419 in the high season.

Further information:

Flight time: Approx 4hrs. There are no direct scheduled flights from London to Rhodes. Olympic Airlines (0870 606 0460, olympicairlines.com) flies to Rhodes via Athens from Heathrow from £200 return including taxes.
Country code: 00 30
Time difference: +2hrs
£1 = €1.44

Package vs independent travel
Click here to read Sally Brown's account of railing through Europe with her daughter