I think they considered this place one of the highlights of their trip to Italy and their kids loved it.
Villa D'Este was created by one of a kind man, the Cardinal Ippolito D'Este, son of that famous Lucretia Borgia daughter of the naughty Spanish Pope Alexander VI Borgia. The cardinal tried to become pope for 5 times in his life, without success. In 1550 he became governor of Tivoli a town just 45 miles from Rome and he moved into a convent connected with the church of St. Maria Maggiore. The new residence was inadequate to his high rank so he sent his architect Pirro Ligorio to study the place.
The result after 20 years was the Villa D'Este, a palace decorated by the best artists of that time: Livio Agresti, Cesare Nebbia and Girolamo Muziano and the astonishing Italian garden with 51 fountains, 398 gushes, 64 waterfalls.
To feed his fountains the cardinal created 3 branches from the aqueduct of the town, which uses the Aniene river water. An hydraulic machine of 500 litres of water per second which still works after centuries.
The most amazing fountains are the Fountain of the Organ which produced music thanking to a subterranean hydraulic system which was recently restored. The Fountain of Ovato with a waterfall under which I used to walk when I was a child.
The one hundred fountains which show strange faces of animals. To end with the scenographical Fountain of Neptune the most photographed fountain of the villa, viewed from the great fishing ponds used once to provide the Cardinal with fresh fish.
The interior of the villa is also a paradise for the art lovers and the decorations and grotesque were painted to delight the eye of the visitor.
The masters involved in the frescoes are the same that can be admired in the Gallery of Maps in the Vatican Museums. Every inch of the interiors are decorated with grotesque and in every corner the family symbol of the cardinal, the lilies and the eagle, can be found as well as the symbol of the grandfather of the cardinal, the bull Borgia.
Practical information: You need to be very determined to arrive to Tivoli with public transportation as the train doesn't run too often to here. From the station you will need to walk a while to arrive to the villa.
With the bus: Reach Ponte Mammolo with the B line of the subway. Here you find the beginning of the buses. They go via highway or via Tiburtina street. It is only known by God if you will find less traffic on one or the other way.
I did it several times and I was alone, so I'm sure you can make it!
If you wish to visit Hadrian Villa, there are buses leaving from the gardens at the entrance of the city near piazza Garibaldi. If you have to make a choice I would always go for the Villa D'Este, but this is a very personal choice.
If you need any further information, contact me through http://www.visitrome.guide