Pasting this list of daylong scenic meanders I posted a couple years ago. Nature doesn't change that quick. This isn't exhaustive, but it'll keep you busy for a season:

Hiking:

East of Hudson--trains from Grand Central:

Breakneck Ridge: Hudson Line to Breakneck Ridge station.

Mt Taurus/Bull Hill: Hudson Line to Cold Spring, trailhead just north of town on Rt 9W. One of these trails eventually joins Breakneck Ridge, but it's a schlep.

Appalachian Trail (NY/CT): Harlem Line to Appalachian Trail station

Appalachian Trail (Bear Mountain): Hudson Line to Manitou

West of Hudson--trains from Hoboken:

Ramapo Dunderberg Trail (Harriman State Park): Port Jervis Line to Tuxedo

Appalachian Trail (Harriman): Port Jervis Line to Harriman. Trailhead about 2 miles south of station on Rt 17.

Schunnemunk Mountain (highest in Hudson Highlands): Port Jervis Line to Salisbury Mills. Trailhead on Otterkill Rd under the huge railroad trestle you just went over on the train.

Biking/meandering:

Duke Farms: NJ Transit Raritan Valley Line from Newark or NY Penn to Raritan. South on Thompson St, west on Somerset, south again on Nevins. Cross the pedestrian bridge and keep going to the Duke Farms gate. Miles of bucolic paths to get lost in.

Harlem Valley Rail Trail: Harlem Line from Grand Central to Wassaic. Trail starts at the station.

D&R canal: NJ Transit Raritan Valley Line from Newark or NY Penn to Bound Brook. Enter the path just over the Raritan River bridge from downtown. Go west/south from there. North/east toward New Brunswick isn't great.

Columbia Trail: Raritan Valley Line from Newark or NY Penn to High Bridge (weekdays only). Walk north on Main St. Trail starts a couple blocks from the station.