Greenwood park has some awesome trails with some nice views. Besides trails they have about 3 gazebos and and indoor cottage that is a party hall. You can rent this hall for any occasion from the town of Ajax and the rates are fairly reasonable.
There is ample parking available close to the indoor cottage and there is more parking available by the main gate. They have a leash free area for dogs, but most of the main trails your dog has to be on a leash.
Bicycles are not allowed on the trails in this park, you can park your bike at the main gate and hike the trails on foot.