NYC to Harriman is okay, but the main route is mostly 9W. You can hop on and off, but it's been a long time and I don't recall any great routes. To get to Fahnestock from there is kind of a straight shot across the Bear Mountain Bridge and down 9D on the other side of the river, to 301 and take that up into Fahnestock. This is more recent stomping ground for me, and there are some of the oldest dirt roads in the country in that neck of the woods, including Sunken Mine, Indian Brook, Old Albany Post, S. Highland, Lane Gate, Canopus Hollow. Totally doable on a Cheviut. Some climbing, but nothing super long or super steep.
One option would be to take Metro North to Beacon (lots to see and do in town, about an hour train ride from Grand Central, get a $5 lifetime bike pass when you buy your ticket) and go out from here. There is a camp ground on the side of Mt. Beacon, so you could do a couple of nice rides from here, or camp in Fahnestock your second night. Could also do the Bear Mountain Bridge to Newburgh Beacon Bridge, which includes a nice winding climb up 218 past West Point, with panoramic views of the Hudson.
The objective with a plan like this would be to avoid spending the majority of that first day on 9W, and the second on 9D. Happy to be a guide for a Saturday. You can contact me off list if you want more info about rides around here, which are numerous and really nice in just about every direction you care to go.
