But for Catherine, husband Michael Douglas and baby Dylan, 20 months - with six homes already in Los Angeles, Beverly Hills, Bermuda, Majorca, Colorado and New York - it needs to be something special. She is believed to be on the look-out for a "Welsh Castle complete with turrets and a banqueting hall" to entertain in.
Which is where the Welsh Development Agency could set in with some handy property advice. Jeff Porter, the WDA's environmental manager based in St Asaph, believes he has just the place.
"We have Gwrych Castle right on our doorstep, standing derelict for many years, in a private ownership and an ideal setting, with all the turret she could want," he said.
The WDA has been trying to market the Castle near Abergele and find a suitable use for the site.
Some Americans have already been to North Wales to view the run down Castle, which overlooks the North Wales coast. It is actually owned by an American - businessman Nick Tavaglione - whose original idea was to turn it into an opera centre. One party from the US considered turning it into a filming graphics production centre. The only other option they had discussed was in Hawaii.
"If anyone has money to invest in this property Catherine Zeta Jones does," Mr Porter said," and just think what an attraction it would be to the area to know that it was owned by such a famous couple. I think it would be ideal for the area."
A Trust set up by Prestatyn schoolboy Mark Baker is commising a feasibility study into the refurbishment of the Castle. Last night one of the Trustees, Coun John Pit, welcomed the WDA's suggestion. "I think it's a marvellous idea - I couldn't think of a better person to come to Abergele, or a better place for her to buy," he said. " Gwrych Castle has a lovely golf course nearby for her husband to enjoy," he said.
Catherine was in Wales a few weeks ago when she took part in the last stages of the Ian Botham walk which raised £800,000 for the Noah's Arch Appeal to help build a children's hospital in Cardiff. That ended in Cardiff Castle, the imposing former home of the Marquis of Bute, now owned by the city.
The ancient monuments agency in Wales Cadw, says that none of it's historic properties were for sale, although one private castle recently seeking a loving owner was Cardigan Castle in West Wales. There has been a 40 year campaign among locals to try and transform the place of historic interest.
Little now remains of the original stone castle which was built in the 12th century and the site is overgrown and off limits to the public. Lord Rhys of Gruffydd, the prince of Deheubarth, Seized the fortress from the Norman's in about 1170 and rebuilt the timber castle in stone. But it was virtually destroyed by Cromwell's army in the 17th century during the English Civil War.
But Catherine Zeta Jones is keen to find a big house so she and her family have somewhere to stay when they visit her Welsh homeland.
She says her Hollywood mansion is a firm attraction for Welsh friends travelling to the USA. "We've always got Welsh rugby players coming over to stay", she said.