We stayed in Athens a few years ago and stayed at Attalos Hotel, which has a rooftop view of the Acropolis. We enjoyed it, but is sold out for late September. Seems like most of the hotels that come recommended in this forum are sold out. Is there any gems that you can share? Our kids are with us this time and want them to experience the ambiance that we had at the Attalos. I'm sure there must be several of these kinds of hotels, but need one that can still accommodate a family of 4. I'll pull up any recommended hotels that you think might work well for us. We always appreciate the kind, well traveled guests that share information that we would have never come across.
I have nothing to suggest, buy have you checked to see what is available on booking.com? I'm afraid the best places people suggest here are not going to have space for 4 people later this month. It might be easier to attack this from the other direction: Post what you see available that appears to work for you, and see whether any posters have comments.
The Arethusa Hotel is worth a look. Similar to the Attalos, but I think a better location.
You might like to look at the Phaedra. It’s smaller than the Attalos but has better views from some rooms and a rooftop bar. It’s in a (more or less) pedestrianised area at the top of Plaka.
Have you tried all the hotels recommended in the RS guidebook?