The best beach in Buyukada itself, in my opinion and in the opinion of my wife, is always friendly staff, very tasty food and towels are always available. The water is very clean and you can dive and there is a playground. We've been there for 3 years in a row and the impressions haven't changed a bit: we'll definitely come back sometime!
A paid beach, which will be reached by boat on the dock, find a young guy in a cowboy hat (he speaks Russian) and ask him for a discount. They will drop 100 lire per person..
You can go to this beach with your own alcohol and food, but do not advertise this. The beach is super. There are a lot of people on weekends