Psili Amos is a fine sandy beach seven kilometres to the south of Samos. It's very shallow, you have to walk far from shore to get into deep water, it is hence well suited for children. It's a sandy beach with shallow waters, sunbeds etc are available. There are a couple taverns near the beach.
On the road from Samos towards Pythagorio, turn left about halfway (there's a signpost), follow the road towards Mykali beach and keep going until you reach Psili Ammos. You are also able to go there by boat from Pythagorio, look for information in the harbour or ask someone in one of the taverns. The trip will take about 30 minutes.