The problem with the train, is you'll have to find a train that allows bikes. I believe bikes are allowed on the metro north that goes through Westchester, dutchess, and putnam.
If you can take your bike on the Sloatsburg line, my route goes right by it and you can easily bike east into Harriman or west towards Warwick and western Orange county.
I, not being a train rider, don't know which lines allow bikes but surely NJTransit may have info on their website.
There's also some flat riding if you can get on the Boonton Line towards Mountainview train station or the Towaco station on 202.... Or the Lincoln park station for that matter, all are on bike friendly roads, although 202 there has no shoulder, it's 2 lanes each way and not too much traffic outside rush hour.
Jay