There is a plethora of childrens activities in Syosset! First check out one of the Syosset Libraries for Story Time, Arts, Crafts, Book Clubs, etc.
Syosset is located in the Town of Oyster Bay which operates many parks and beaches. They also operate summer camps in the summer and offer childrens concerts, plays and other events. This is their website:
http://oysterbaytown.com/places-to-go-things-to-do/The Syosset/ Woodbury Park on Jericho Turnpike has a large playground, an enormous public pool, and a great public outdoor skating rink. Cantiague Park on John Street in Hicksville (10 min away) has an indoor skating rink, a large outdoor pool, a 9 hole Golf Course and a miniature Golf Course.
Off the beaten path is the Cold Spring Harbor Fish Hatchery. When your child tire of the indoor exhibits, there are also outdoor exhibits to explore and then go up the stairs to the duck pond to visit the ducks and swans.
That is just a handful of suggestions!