Here are some staff picks from the Yonkers REI team:
Harriman/ Bear Mountain State Park
Happy hiking! If you want more recommendations just call or come by the store!
Storm King on the west side of the river is my favorite. It's less steep than Breakneck or Anthony's Nose if you're looking for something easier.
Naturebetty, here’s a bunch listed at NY/NJTC. There are many more than what’s on this list. https://www.nynjtc.org/view/hike?field_difficulty_value=Easy+to+Moderate&field_features_items_value=...
Bonticou crag in thye Gunks. It is not a climbing route but rather a moderate hike that offers some safe exposure at the top of the ridge.