To the OP, if I only had one visit to the Adirondacks I would travel up Rt 73 from I87 through Keene Valley into Lake Placid. From there you can book a hotel or inn. I recommend hiking any of the amazing trails within five miles of LP. Lake Placid is famous for holding the Winter Olympics in 1980. If you go in September you will likely never forget the views. Many of the trails lead up to the summits of smaller mountains. Others lead up to larger mountains. You would have to research further on how to arrange getting there. I would rent a car in Albany and head straight up I87, once again, to Rt 73.
Best of luck!
https://en.m.wikipedia.org/wiki/New_York_State_Route_73