There are some very popular trailheads near Mohonk Mountain house including the Lemon Squeeze and the Skytop Tower hike. A few other great hiking options are listed here: https://www.theoutbound.com/united-states/new-york/new-paltz/hiking
If you are staying for multiple days, we'd definitely recommend you check out this cozy Italian restaurant. They have super tasty food and a great wine list. They are also so friendly! We go here every time we visit. Would recommend you reserve ahead of time as they tend to get quite busy.
Great, casual brunch / lunch spot. Super friendly service and a wide selection of options.
Another really great hiking area. Some trail options can be found here: https://www.alltrails.com/parks/us/new-york/minnewaska-state-park-preserve
Cute small farm with great produce and fresh flowers. You could stop by on your way back!