You can anchor
off Alkyes if it's the normal conditions of the prevailing NW and it's going to calm down after dark.
I went into Vromi and there is very limited anchoring
possibilities, so I suspect you'll be lucky to get a spot. I'd only try that if you have the time to go to the other side of the island after lucking out on a spot.
If you have a no wind
day and the forecast
is for the same overnight there is perhaps reason why you couldn't stay the night in Shipwreck bay.
Also if there are winds like there are today, then it also is probably ok to stay there.
If I was to stay overnight I'd anchor in the middle and then move to the west side in the morning just in case the day trippers start arriving