Being a guest in this area and coming from the Netherlands I tried to do some bicycling.
Unfortunately I found out that one has to use special trail and above that I discovered that this trail doesn't exist. The people at the Vanderbilt mansion had no idea what I was talking about !

"Your description states that this is a biking and hiking trail so we took our bikes to Riverfront Park in Hyde Park and discovered that there is no biking allowed within Vanderbilt, Roosevelt or Vallkill National Historic Sites, hiking only. According to their trail map, there is biking only on the wooded section between Rte 9 & 9G, from FDR Home to Vallkill."

"When I visited this trail I parked at Riverfront Park on County Route 41, which is midway between the “Vanderbilt Loop” and “Roosevelt Trail” segments of the trail network.

Riverfront Park has ample public parking facilities, a nice covered picnic pavilion, a small children’s playground, and wonderful views of the Hudson River. If you’re a train buff, Amtrak trains bound for Albany, NY and other points north pass directly by the park. An added plus for train buffs is the old railroad station being restored right next to the park!

The 2.4-mile long “Vanderbilt Loop” is just north of Riverfront Park. A short road shoulder walk (0.2 miles) is necessary to get there. This trail loop proceeds on a dirt path just above sea level as you head north from Riverfront, and then makes its way along a ridgeline overlooking the river when heading back to Riverfront. The upper trail segment is mostly on a paved path, which makes its way through the meticulously manicured grounds of the former Vanderbilt Estate. Breathtaking views of the Hudson River and opposite shoreline are available from several points along the upper trail.

The 1.2-mile long “Roosevelt Trail” is 0.6 miles south of Riverfront Park, also requiring a road shoulder walk for connection. This trail segment is cuts through a very heavily wooded area as it makes its way to Franklin D. Roosevelt National Historic Site. Gorgeous views of the Hudson River and opposite shoreline may be found just south of FDR’s former home.

Once you reach the FDR National Historic Site, you can easily make your way across US Route 9 and connect to the 2.5-mile long “Val-Kill Trail” and 1.5-mile long “Val-Kill Loop.” Regardless of the posted “No Motorized Vehicles” signs, The “Val-Kill Trail” is heavily used by ATVs; use caution if you intend to walk this portion of the route. National Park Service rangers also warned me that much of the somewhat overgrown “Val-Kill Trail” is heavily infested with deer ticks.

Bicycles are permitted only on the “Val-Kill Trail.” Dogs are permitted everywhere as long as they’re leashed. Restroom facilities are available at the Vanderbilt, FDR, and Val-Kill National Historic Sites.

You’ll need ¾ of a day to travel the entire trail network by foot. Enjoy!"