Bureaucratic Manners
The Greek immigration system is confusing, full of pitfalls, and with uneven success at overcoming the subtle racism directed at the hordes of applicants less fortunate than you. Many people hire a lawyer to chat up the correct person (or whatever it is immigration lawyers do...). If you go on your own to apply for the permit, dress in upper-class clothes and bring multiple copies of everything in your briefcase. Waiting in line is optional, apparently, so do not be afraid to ask directly for help, ideally from an employee of the opposite sex. Smile bravely, and behave as if convinced that they will be relieved to deal with you, a respectable and legal person with a straightforward application.
Traveling Without a Residence Permit
You can easily buy a one-time extension of your stay as a non-working tourist from the Aliens Police, provided you do so before your three months are up, but it is expensive.
If you have overstayed your three months, and need to leave Greece and return, it is somewhat safer to fly to the U.S. through another Schengen destination like France or Italy (but not the UK). You will be stamped out of the Schengen Zone by a passport control officer who sees your U.S. passport and onward ticket as an indication that you are not his country's problem. On the other hand, going directly to the U.S. you will pass through Greek passport control, which may look at the entry and exit stamps in your passport, fine you for overstaying your allotted time, and even bar your reentry. Beware, however. The Schengen Zone will one day be networked into a truly organized system, and the loopholes will narrow greatly.
Health Certificate
Among the more pointless bureaucratic formalities for a residence permit is documenting that you are not a threat to public health. For the visa from the Greek Embassy in Washington, that requires a letter from your doctor. For the residence permit once you reach Greece, however, that means in practice a chest x-ray from an authorized Greek state hospital.
In Athens, the health certificate can be obtained at the "Agia Eleni" Spiliopouleio Pathological Hospital, at Dimitri Soutsou 21 (between Plateia Mavili and Ambelokipous Metro station), telephone 210 641 0445-7, between 0900 and 1200 Monday-Friday. No appointment is necessary. However, call ahead to confirm x-ray unit is working. Cost (2004) is ˆ3 for the certificate and ˆ4,50 for a mandatory chest x-ray. Bring passport and two photographs.
The chest x-ray can be obtained from the Institute for Thoracic Research at Averof 12A, 1st floor (near 3 September Ave, between Omonia and Viktoria Metro stations), telephone 210 821 0653, between 0800 and 1200 Monday-Friday. Bring passport and photograph. Cost is ˆ4,50. The x-ray can be picked up the next day between 1200 and 1400, 2nd floor.