From Agios Nikolaos, after leaving the sheltered beach Amoudi behind and following the road leading to Elounda, you will soon meet the enclosed bay of Katholiko, formed between the Hotel Minos Palace and the Cape Nissi. It is a small pebbly and sandy cove, which is mainly used as a harbor for boats (and is not well organized). There is a playground on the beach. Katholiko is generally avoided by swimmers (due to the boats), but still it's allowed to swim here, although there are many better choices nearby.
At the Cape Nissi there is the Byzantine church of Saint Nicholas, after which the town Agios Nikolaos gets its name. From Katholiko starts a seaside road ending in the rocky tip of Cape Nissi with the WW2 pillboxes. From there the views to the small island Agii Pantes (All Saints) and Mikronissi are great.
Inside the area of Minos Palace hotel there is a nice sandy beach, which is well organized by the hotel. Access is free, of course, as in all beaches of Greece. Note that the beach is not directly visible from the main road.