Plenty of parks in Hornsby. If you live near Hornsby "CBD" (around the Westfield shopping centre) the best for younger kids (playground type park) are Beatrice Thomson Park (intersection Water St & Albert St) and corner Mildred Ave & Jersey St North (a bit further away).
For a larger type park for sports, BBQ, and canoe-ing, the best is Ku-ring-gai Chase National Park (just a few minutes drives away - worth a visit).
Hornsby is surrounded by an abundance of parks and playgrounds. Parks within Hornsby are Lisgar Gardens which is located on Lisgar Road, Hornsby Park which is located on Pacific Highway, Holman Park which is located on the corner of Northcote Road and Sherbrook Road and Ginger Meggs Park which is located on Valley Road. If you are looking for a park with a playground as well as BBQ facilities, Hornsby Park has both. Hornsby Heights also has a large variety of parks to visit. Rofe Park is located on Galston Road and has a leash-free dog area. Crosslands Reserve, a camping and picnic area is at the northern end of Hornsby Heights off Somerville Road.