They're rich in ancient history, but poor in modern money. Pam Neville writes that the home of democracy needs our help.
Everyone wanted euros. They accepted credit cards in most places, but cash was king. The banks were closed. Greek people could withdraw a maximum of 60 ($100) a day from an ATM. Some ATMs ran dry, many ran out of 10 notes, which meant the de facto maximum was only 50.
It was not a problem for tourists. With a foreign card, we could withdraw as much as we liked. Only once did I experience an empty ATM on my July visit, but the machine around the corner obliged.
On the five Greek islands I visited, the locals were uniformly smiling and welcoming, but concerned and eager to talk about Greece's economic woes. To a man and woman - whether they had voted yes or no in the referendum on the bail-out - they said, "We don't know what will happen."
Now the bail-out deal has been signed and the banks are open, albeit with severe restrictions on money transfer and withdrawals, but people are still saying the same thing.
There is no confidence that Greece will cope with the new austerity and debt-payment regime, but it's universally agreed that keeping the tourists coming is vital.
Our young female hotelier on Santorini, with an economics degree, was aghast at the bail-out terms. She was an oxi, or no, voter and wanted to dump the euro and return to the drachma. Rich European nations, especially the hard-bargaining Germans, were to blame for Greece's plight, she said. (A recent story in a British newspaper about the anti-German sentiment was headed "Don't tell the cook we're German".
The hotelier's views were the direct opposite of the academic archaeologist who led our tour of Delphi on the Greek mainland a few days earlier. He believed leaving the eurozone would be folly. "So long as the tourists come, we will work our way out of this," he said.
"We are not complaining," said the rental car man who furnished a small Hyundai to drive around the island of Paros.
That night in Naoussa a festival of dancers from around Greece welcomed the summer. Introducing the performers, a woman described the current crisis as "Greece's darkest hour in 40 years" - a reference to the Colonels Coup of 1967 - but it doesn't stop the dancing.
There are no figures yet to suggest tourist numbers were down this northern summer but some popular places seemed to me to be pleasantly uncrowded. Not the hot spots like Santorini and Mykonos, however, especially when the cruise ships were in port.
Extra flights from Britain kept up the numbers on Mykonos, famous for its gay scene. Among the hundreds of tourists of all ages and nationalities at the ferry port, a young fellow's T-shirt taunted "I've gone to Mykonos, Bitch".
It was fun and games as usual on all the main Greek islands. The people, the food, the wine, the sunshine and beaches: the economic crisis doesn't change them. Strikes, protests and riots were confined to a small area of Athens. It seems every Greek understood that frightening or inconveniencing tourists would be a bad move. Tourism is everything. Go now, they need you.