September is probably the best month of the year to visit Switzerland, I get there almost every year in September.
<<"We will be there in September. Just not sure about travel times between sites, as I would like to squeeze in two "visits" to places in one day.">>
Lucas said it all.
Use the timetable:
It covers all the trains, buses, public transport cableways, and lake boats in Switzerland.
Be sure to read the instruction page at that link, and note that the computer defaults to the fastest route.
You can enter intermediate stops in the"via" box to force the route to a slower one....as mos of the scenic ones are.
Boats are slow, so you sometimes have to work the menus to force it to show ships.
If you use this map, you can see the train lines (zoom in):
map.search.ch/index.en .html?retry=1&pos=571608,157 752&z=32
The first part of the Golden Pass route, between approximately Montbovon ( or maybe Zweisimmen) and Montreux is very scenic. You could go partway and turn around to come back down to the lake. Or, if you go to Gruyeres, return via Montbovon and Montreux to get to the lake, then a fast train to Geneva.
In September, especially late in the day withe the slanting sunlight, the views from the "Wine Train" going up from Vevey to Puidoux can be very nice, if brief.
It connects at the bottom with trains through Vevey, and at the top with local trains to Lausanne, and thence back to Geneva.