Buses drive fairly regularly along the north coast between Samos-town and Karlóvasi.
The prices are reasonable. If you would rather not travel by bus, taxis are a good alternative. They are likewise not expensive.
Naturally a car is the best solution for families with small children.
Also because the beaches are not in direct proximity of the village (at least 5 km) and it is not nice to walk with children along the main street.