Grown up in Murten I know and love this area, here are some of my favourite places:
What kids like!
A fine piece of Nidelkuchen is of course also part of it. The best is at Aebersold.
Swimming at the lake, we love Salavaux Plage.
A visit to the caves on Mont Vully is also a must!
A boat trip to Lake Neuchâtel.
What else I like to do at the lake:
At "Bise Noire" in Murten you can rent the boards for "Stand up paddle". My sister and I now have our own and try to get on the board as often as possible.
Of course there is much more to discover....
Maybe we'll meet in Murten, I'm a city guide here too.