I have been to Syros in the summer and autumn months, and although the Greek islands' typically have a better nightlife scene in the summer, Syros (or shall I say, Ermoupolis), has a pretty good scene all year round, any day of the week.
There are a few good bars around the port area in Ermoupolis which are thriving of locals, other Greek tourists and handfuls of international tourists.
They are open until very late all year round.
It appears it's very safe for women to be out all night also. I noticed many walking through the narrow streets of Ermoupolis at 4am in the morning! :)
Dress Code: Casual to smart casual.
If you belong to that particular category of persons who like gambling and, during your holidays, you can not miss the opportunity to pay a visit to the local casino, Syros will reward you plainfully!
A wonderful neoclassical building, at the port entrance (you only need to hop from your boat and you will get into the casino!), houses the Casino of Syros.You can experience all kind of "gambling pleasures": starting from roulette, black jack to slot machines.
Sorry, I am not an expert, so I can not give you any further information!
Dress Code: Tie is not required, but try to be properly dressed.No shorts and flip-flops!