Hi, I am not sure if you have children, but I often take my family either to the area just outside the playground of Chinagarten. It is gorgeous and a huge space with a playground to entertain the little ones.
exactly opposite the China garden on the other side of the lake a little further then the Rote Fabrik there is a beautiful big park with playground and loads of grass with plenty of space for pick nicks near the water...
Easy by train and probably just about one hour drive is Arth Goldau Tierpark, there are many picnic spots in the park and the animals (safe ones) roam amongst the visitors. http://www.tierpark.ch/english/index.htm
Alternatively park up at Arth Goldau and take the train up the Rigi. Amazing views and a great place for a picnic........take some warm clothes if you try this!
I am going to Weggis with friends this weekend - I heard it's beautiful.
Weggis is beautiful, especially if arriving by steamship, some good restaurants by the lakeside (think we ate the hotel Gottard last time which was excellent though a little more formal than we would normally go for.