Hi Sylvia,

Have a look at http://www.refuges.info/

I think you will find something close-by (Jura for ex.)

Good luck, Patrick

Hello Sylvia, 

Here's a refuge very close by in the Jura above Thoiry...

http://homepage.bluewin.ch/curson/index.html

There is the Cabane de Carroz which is 1.5 hours from la Givrine but you have to prepare your own meal and bring up the food, the hut warden only provides soup or tea coffee.  All the equipment is there for cooking or making a fondu.  La Givrine can be reached by train. 

It is not a 'family friendly' hut because this description tends to refer to huts where there is easy climbing for children in the vicinity but it is a nice hut with beautioful easy Jura walking in the vicinity.

It belongs to the Geneva section of the Swiss Alpine Club but is not listed on the CAS website because it is privately owned

http://www.cas-geneve.ch/pdf/Cab-CASGE-Chalets.pdf

I  have passed the Chalet to Curzon and it seems OK but other to look at in Hte Savoie are chalet desSales, Chalet d'Anterne Alfred Wills, there is also a refuge at the lac Blanc above Chamonix but not sure how often it is open. 

Thanks much for all the tips!  With the weather like it is, we will probably be trying for another weekend.

Here's another website I found on family friendly huts.  Nothing very close to Geneva, though.

http://www.sac-cas.ch/huetten/huetteninformationen/familienfreundliche-sac-huetten.html