Upvote:4
There are two popular options not too far from Istanbul.
The Princes Islands (Adalar), are a 90 minutes ferry ride from the center of Istanbul. In principle the islands are quiet as there are no private motor vehicles allowed there. However, they can be crowded in July and August. In that period, it is better to avoid going there on a weekend.
On the Black Sea you can go to Kilyos (40 km from central Istanbul). You can get there by ferry and bus. It's a pleasant trip.
For more information you can have a look at the following page:
http://www.turkeytravelplanner.com/go/Istanbul/Sights/beaches.html