There is a wonderful camping between the villages of Evolène and Les Haudères in the fabulous Val d'Hérens. Take the train to Sion, then the bus up to Evolène (a great ride) and just ask the bus driver to stop you at the campsite- shops, restaurants, etc, and both villages are easy walking distance- and the bus will take you up to Arolla where you can walk by the glacier, or the other way to walk practically on the flat to the Ferpècles glacier.
Depends on what you ae looking for - if you are after a lake there are camping places at Murg and Walenstadt on the Wallensee - both walking distances from the train station - Murg in particular. If you want to closer to hope you can get a bus from Stettbach to camping places on the Greifensee!!!
TCS have camping places and with an address you'll be able to SBB.ch for the travel time. For example TCS Camping Bellinzona at Bosco di Molinazzo is right opposite a bus stop
There are also half a dozen campsites about 1km of Tenero station on the Lago Maggiore. St2lemans will be happy to shuttle you down to the campsite
I went to a pretty well supplied campsite in Sarnan. Although I did get a taxi from the station to the campsite as it was around 3/4k, which is walkable only when you are not lugging the amount of stuff I take camping. When I went to leave the reception was a little confused about me asking for a taxi and the taxi driver was not sure where to pick up, so I don't think not driving to that site is common. But great pools.
It is great. Small child friendly shallow beaches, restaurant, shop, lots of young families. A cycle path/footpath to the village where there is a cheese shop etc.
We got the train to Yverdon les Bains and from there a taxi.
You got some good ideas already. Not sure if you have done that before but Zurich has also a really nice one. Its in Wollishofen and directly at the lake! Other option would be to check out Rekadörfer. They will provide you with everything you need if travelling with small children.
This may be coming too late but I just saw this post and thought I'd share ourr experience.
We camped a lot this summer, mostly in Switzerland and the Eienwaldi campsite in Engelberg was probably the most incredible place for us and the kids- lots of outdoor activities for kids, own football grounds, small paddle pood, playpark, ping pong table. Totally accessible- we had no probelms with a wheelchair at all.
For the parents- gorgeous views, Titlis at a stone's throw and a small thermal pool in an adjacent hotel.
Well be back
(ps. we cam back there on a cold September weekend and it was still packed with people, mainly families- that's got to mean something)