You are free to go swimming wherever you want to except from private gardens. The best spots are probably on the west side of the island.
There is a small beach on the west side of the island that is pointed out with a sign from the trail Sörmlandsleden. The beach is an ideal spot for families with small children because of it’s shallowness and sandy seafloor.
Depending on the wind there might be seaweed on the beach. Use the rake and put it in a pile aside and enjoy the swimming.
Sävö is the most northern island in the group of islands, Hartsö-Ringsö-Långö-Sävö. There are excellent waters to paddle in the surroundings. A short tour will take you around the island.
If you feel like going a longer distance the channel between Långö and Ringsö will take you further in a beautiful bay of small islands. If you don’t have a canoe of your own there are possibilities to rent one on the mainland, Hälgö kajak.