We're a couple and we'll land in Istanbul on the night of the 10th of August for five days. We'd like to find cheap accommodation (possibly around €30, meaning €15 each) either in the city or in a nice village on the beach nearby. Since it's quite hot in August we'd prefer a place with air-conditioning or big windows in a green and windy area.
30 euros is possible, but you'll have to search for it. Air conditioning and big windows are a bit specific, which means you'll simply have to search longer.
Try http://www.hotelscombined.com/ for getting, often, the best rates on hotels.
Try http://www.airbnb.com/ if you're ok with staying in someone spare bedroom, or garden bungalow.
Typically, the latter will give you much better value for money, particularly if you're ok with not staying in the tourist center of Istanbul (which is Sultanahmet).
Did you try looking on airbnb.com? here you have a few options on your dates: https://www.airbnb.com/s/Istanbul--Turkey?checkin=08%2F10%2F2014&checkout=08%2F15%2F2014&guests=2&price_max=30