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You can just about fit in all the castles on Lake Thun in 1 day – it’s not a very big lake.
I’d say Schadau is probably the missable one
Thun, Hunegg and Oberhofen are all within 10 minutes of each other on bus route 21 along the north side of the lake, Spiez is 30 minutes by boat from Oberhofen (decent timetable in summer months so OK for June) or main line train from Thun
This website could help you choose which ones to miss out if necessary.
http://www.thunerseeschloesse r.ch/en/
as the website says: Welcome to the official website of the Lake Thun castles. Five castles, each with its own unique personality, connected by one of the most beautiful lakes of Switzerland, and all accessible in less than one hour.
There is nowhere else like it in the world.