I'm visiting Santorini on late August and i'm looking for a villa to stay. Not crowded hotels and away from all the well known tourist areas!
We are a group of 8 and we just want a comfortable, private and quiet place to stay, swim and spend our days off!!!
There are sites like villarenters but late August booking a private villa for 8 just weeks before is going to cost you thousands. Maybe two 4's might be better but not much.
If you want more reasonably priced you could try the Accommodation link above, something like the Villa Manos but you are not going to find anywhere reasonably priced like you might have if you had booked maybe four months ago.