I am a Greek-American who has been living in Athens for over 25 years. Therefore I am probably well qualified to provide you with appropriate information on moving to Greece.
Generally speaking, I would suggest that moving to Greece is not such a hot idea, but, quite a few people have done and haven't regretted it. At least not yet.
I am going to assume that you do not have any Greek heritage and that you are an American citizen. Based on this assumption I must tell you that your prospects for living the kind of life style you have grown accustomed to in the US are dismal at best.
There are quite a few Americans living and working in Athens but the overwhelming majority of them were hired in the U.S. by American firms with operations in Greece. The companies involved take care of all the formalities, ie. work permits, tax issues, etc. Those Americans receive salaries which are comparable to US standards and they live quite comfortably. Therefore one way of moving to Greece is to find employment with a large US based corporation which would like to send you to Greece.
The only other way would be if you were to marry a Greek. If you are married to a Greek citizen then the Greek authorities must issue you a residency permit and work permit for any job you might be interested in pursuing. Just being "engaged" doesn't count for anything. You can either get married in a civil ceremony or in a church, but you must be married. A very important thing to remember is that should you or your wife decide to seperate then your residency and work permits may be rescinded.
As to the salary situation, that is rather mediocre. Unless you have a very special field of expertise for which you can demand a rather high salary you will otherwise be very limited as far as renumeration is concerned. Also, it would be wise to note that the unemployment situation in Greece is at this time the worst it has been since WWII. Jobs are very hard to come by and since I am assuming that your Greek is rather limited it will be very difficult for you to find a job for the first year or more.
Obviously I am amongst those who believe that moving to Greece will bring upon you nothing BUT problems, but if you want it bad enough I suppose you can overcome those problems.
Just about every major U.S. computer hardware and software company conducts business in Greece. Microsoft, IBM, Compaq, Apple, etc. If you have atalent one of these companies need your best bet would be to put together a resume and send it to every company you can think of with a cover letter in which you will indicate to them that you are interested in securing a position with their operations in Greece.
Working off the Books
Things have become especially difficult for Americans because Greece has signed an international treaty with the other European Union countries called the "Schengen Treaty". Basically, this treaty places strict restraints on all member nations on whom they allow to reside in their country. The bottom line is that you will not be able to get legal residency status here in Greece unless you can find a job working for a big firm that would be interested in you enough to go to the trouble of getting a residency and work permit for you.
You could work off the books, but you would always run the risk of being caught and deported. If this were to happen, you would not be allowed entry into Greece again for 5 years. Many young people do go to the islands to find jobs as waitors and dishwashers in bars, restaurants and hotels but landing a job is a matter of luck and being in the right place at the right time and you should not go to Greece with no money expecting to earn it there.
Regards from sunny Athens,