Firstly you will need a car if you dont have one already, since the train can be tedious and expensive, albeit reliable.
The obilgatory castles at Montreux and Nyon come to mind... more info here : https://www.lake-geneva-switzerland.com/top-sights/historic-buildings/top-chateaux-castles-fortresses-on-lake-geneva/
It might be worth taking a day trip (hours drive) from Montreux to Evian... to see the spring, and evian museum and remember to take your water bottles for free top ups! its in France so remember Euros for the touristy t-shirts etc.
Taking a drive into Valais, and up to either Verbier or Nendaz and having a mountain walk... at nendaz especially there is a relatively flat route at 1400m that follows a former water stream along the mountains with a few opportunites at some chalet cafes to stop off for a hot chocolate and cake. its a beautiful walk with fabulous scenery.
You could take a drive to Nyon and take a ferry to Yvoire, a historic french village, very pretty, but very touristy.
The website posted above has many more suggestions.
Enjoy the area.
Sep 2, 22 13:05