Well I`m sure Harriman State Park and if you dont mind crowds Bear Mtn State Park would be well within your range. Harriman would fit your needs I believe since they have everything from mtn views to nice trails along lakes and streams. The trails can be everything from an old logging road to a single track path that requires some scrambling up rocks. So it has everything to offer the most to least experienced.
You can get there using either the George Washington Bridge or the Tappan Zee Bridge. There are trail heads along the Palisades Parkway and rt 17/seven lakes drive.
If you need any details or have any other questions feel free to email me.
