There are 2 islands with casinos.  They are the islands of Syros and Rhodes.  Syros is the capital of the "Cyclades" group of islands amongst which are the islands of "Mykonos", "Paros", "Ios", and "Santorini".  Therefore if you are thinking about visiting any of these islands you might be well advised to choose Syros for making your "gambling pit-stop".  You can either fly or take a ferry boat ride from Athens to Syros and then island hop from there using the extensive ferry boat and/or high speed hydrofoil service between the islands in the group.

The island of Rhodes, on the other hand, is also well worth the effort. The ferry ride is over 16 hours from Athens therefore it would be preferable to fly there.  Unlike Syros, Rhodes is a very large island with a great deal to offer for every visitor.  It has beaches, water sports, ancient ruins, medieval castles, byzantine churches, and much more.

Unfortunately the casinos in Greece are indeed European style in that they are rather dull as compared to U.S. style casinos.  No fancy shows or free drinks or major events, just plain gambling without any of the frills that Americans have grown accustomed to.

Black tie is no longer required.  Moderate casual attire is acceptable to gain access to the regular gaming room, but, if you wish to rub elbows with the "heavy hitters" in the V.I.P. lounges then you will indeed need to be accordingly attired.

The minimum on most tables is  about 3 euros, but there are always a few tables with lower minimums.  This applies to the regular gaming rooms.  In the V.I.P. lounges the minimums are much higher.

There is also a casio in Parnitha right outside of Athens and another in Loutraki.

I hope this information is of some help to you. 

Regards from sunny Athens,
Tom