There are no beaches in center of Galatas. The best and the closest are on the road east of town. The first little beach is about 1,3 kilometers from center of Galatas. It is named Bouja. It is only a small beach. There is no taverna or bar or even a kiosk. Just a small beach where you can swim. Sandy bottom.
Next beach you come to is Plaka, about 2,2 kilometers from center of Galatas. I think this is a nice little beach. Sandy bottom, a pier where children jump from. There is a nice little taverna where you can have something to eat.
The last beach within reasonable distance is Aliki. This is perhaps the best beach in the area. It is about 3 kilometers from center of Galatas. Here you have the most shallow beach. They have two tavernas, a watersport-center, and a pool. It is possible to go here by taxi-boat. I have more photos from Aliki on my Poros-page about beaches: Aliki