Great trip. Unless you want to ride the Lake Shore Limited and the Adirondack end-to-end (which I would understand), you could stay overnight any place between Schenectady and New York City. When I took the Lake Shore Limited to connect to the Adirondack, I stayed at the Rhinecliff in (surprise) Rhinecliff. It was completely satisfactory (and a touch quirky) if unspectacular, it was an easy walk from the station, it was cheaper than New York hotels, and it allowed for a less hectic morning when catching the Adirondack. (A nice breakfast was included.) I would certainly stay there again if I were connecting from the Lake Shore Limited to the Adirondack.
This past May, I think I picked a supper time before the first meal and it applied to every night. Maybe I needed to request it every night, but certainly I ate at the early seating every night.