I love Nyon, BUT! since you have children I have a better offer
First option is Gruyere - the hometown of the popular Swiss cheese. The town of Gruyere by itself is amazing, it's like a fairytale come through. They have a real castle which you can visit and take photos from the very top.
But most importantly you can go to La Maison de Gruyere to show your kids how the cheese is made - it's a great and entertaining activity.
If you are travelling with teenagers you can stop by the museum of Giger - the guy who created Aliens. A very atmospheric place. They also have a thematic bar across the street which looks really cool.
Finally you can enjoy a fondue or raclette made from gruyere cheese in a local restaurant. The driving time from Geneva to Gruyere is about 2-3 hours.
Second option is to go to Lausanne's museum of olympic games. I went there with my son and he loved it (he is 8 and very much into sports). It's filled with priceless artefacts and items and tells you a story about how the games came into existence. As an adult I found it very interesting, too (I rented an audio guide).
I would definitely do both these things, to be honest, but definitely not on a same day!