If you want to start doing self-contained touring but want to start small, here's the perfect bike overnight. Day 1 is quite easy, using the South & North County and Putnam Trailways to just above Brewster (Sears Corner). It's 55 miles and 2200 vertical feet. Day 2 is more challenging (but shorter - about 42 miles and 2900 vertical feet) with more climbing and several steeper sections, but it goes past beautiful lakes and through state forests. Just make sure you have low gears. Since you're just doing one overnight at a motel, you won't need to pack a lot. This tour could be done on a road bike (as long as it's geared low) with either a seatpost rack and small panniers or something like a Revelate Designs touring seat bag.
The mapped route for Day 1 starts at the Kingsbridge Rd. station on the D train, which has elevators to get your loaded bike easily up to street level. You could also take the #1 to 231st St., where there is an elevator down to the street, and follow Broadway up to Radford > McLean > Tibbetts and onto the trailway. Follow cue sheet from there. Lunch is in Yorktown - there's a little park with picnic table across from the deli, and there's an excellent bike shop just up Commerce St. from the trail.
Overnight is at the Bel Air Motel - very basic, but you can bring the bike into your room. 7 Stars Restaurant is right across the street - a quite decent, friendly diner, good for dinner & breakfast.
Day 2 is a roundabout way to get to Cold Spring that takes in some of the prettiest scenery in Putnam County. (RWGPS link: https://ridewithgps.com/routes/28743860.) The mileage is shorter to allow time for photo ops and rest breaks after climbs. Make sure you have snack food & plenty of water - there's no place to restock between Carmel & Cold Spring. The pit stop in Fahnstock Park is a picnic area with porta-sans. Once in Cold Spring there are lots of choices for food, beer & ice cream. Then take Metro North back to the city. (Bring bungee cords for the train.)
cw - 10/2018