The dome is put on in Albany, and runs north to Montreal on Thursday, Saturday and Monday. It runs south from Montreal to Albany on Friday, Sunday and Tuesday. Also it will only be there until (IIRC) the 3rd week in October!
I have not ridden the Adirondack when the Great Dome was on, but I used to ride it often when the old bubble top dome was on in the 70's and 80's. I was almost the only one up top for most of the route! (And the bubble top dome is only 1/3 of the car!)
The most scenic portion is just north of Whitehall to just south of Plattsburgh - where it follows the shoreline of Lake Champlain (right side)! Although this whole route is scenic!
I'll be on it on October 18 and 19.