After idly wondering about Syros for years, about 5 years ago, in June, I finally stopped at Syros for 2 days, on my way back from Naxos to Athens. I wanted very much to see the famous Town Plaza with church towers crowning the hill behind ... the famous view always shown in guide books. My visit was an insight into a very different island. I stayed in Ermopoulis, found a room in the Old Town area to the right of the Square, in an old Decayed SeaCaptain's Mansion (In a former drawing room - chandelier, 20-foot ceiling, parquet floors and NO lamps of any kind!). That area very much reflects the former wealth, though only partially restored. I wandered the old town, spent the evening in the square which truly IS gorgeous, next day took a bus route that went around the whole Island, & got off at a beach for lunch & a swim.
What I learned:
• Syros is FOR the Greeks, 99% of visitors are Greek, they don't much care about nonGreeks, nor welcome them. I'd heard people say they had a great time there, but further inquiry revealed they went there with GREEK relatives.
• Island in 19th C was THE business Center of the Cyclades, very prosperous -- its orientation STILL. I wanted to find some art, crafts, creative local items -- walked the town for an HOUR and found Not a single gallery or arts-oriented shop -- lots of banks, realty, lawyers offices. Main evidence of The Arts: the miniature La Scala, pridefully built by those 19thC merchants.
• Beaches are Meh, compared to Naxos... smallish & crowded. No one speaks English.
A last indicator: It's impossible to take a photo in that impressive Town Square that fully reveals it, PLUS the churches above, so naturally, I wanted a postcard showing the aerial view. During that fruitless hour-long trudge through Ermopoulis streets, I not only didn't find that postal, I found NO postcards, or Guide books, Or calendars with views, Anywhere, Only when I was at the pier, waiting my Blue Star ferry did I see a candy store right by a dock for day-trips, and it had a postcard rack on the counter. That was IT. But of course, Syros Greeks don't buy postcards of their own island, so why bother.
I've visited over 25 Islands in Greece, some of them 7-10 times, and never before have I felt excluded. I don't mean hostility, I just mean I felt totally ignored. Perhaps since there are 4 of you, and you'll stay somewhere upscale, it will be different. I have been to many less-known islands, not the ones you mention ... places like Samos, Chios, Serifos, Kia ... and on every other island I've felt a welcome, had rewarding interactions, and look forward to returning if I'm fortunate. I have no urge to revisit Syros... I have my postcard, that's enough.