Mid January most years is a safe choice. But later is better. You just have to avoid the European school holidays, in any case February 18 - March 4.
Geneva has a good (train) connection to iconic places such as Chamonix, Verbier, Zermatt, Les Trois Vallées and Espace Killy (Val d'Isère & Tignes). Those places have massive vertical and a lot of off-piste terrain, if there's enough snow. But since most of the terrain is above th tree line (which is around 1800 meters above sea level, in the Alps), there's a bigger chanc of white-outs if it snows. And the terrain needs more accumulated snow to open the easy off-piste terrain (rocks underneath in stead of nice Sound of Music-like alpine meadows) and generally steeper runs.
Zürich connects well to places like the Jungfrau Region (Wengen, the Eiger), St. Mortiz, Davos, but also St. Anton am Arlberg in Austria. All are easy train rides from Zürich. All are very nice to ski and everything should be open by then in a normal snow season. But the terrain in these places is a bit less extreme. More skiing below the treeline and mostly alpine meadows in between. So not much snow is needed to go off-piste. Not that snow should be a problem, though.
St. Anton may be the best option for you and your family. For skiers your level, it offers great groomed runs (about 350 km of them, since St. Anton and Zürs will be connected by a new gondola next season - all in the same ski pass) and even greater off-piset, with many so-called 'ski-routes': ungroomed off-piste runs that are patroled and secured. So you don't need a guide or avalanche gear to ski off-piste. And they are well marked on the trail map as well.
The direct train from Zürich stops at the station in the centre of town, which is much livelier than any of the Swiss or French towns. And since you're traveling with two teen girls, I think the much younger international, sportly and easy-going crowd will appeal to them more. As do famous après-ski places such as The Crazy Kangeroo and the Mooserwirt. And just rent skis in St. Anton. Just about any shop offers high-end piste or allmountain skis (including Bonafide and similar) and also freeride skis if you want. It is, after all, the freeride capital of Austria. If you need more info on that, just PM me.
So my advice is: book your flight to Zürich now and choose a final destination in November or so. If you avoid the holidays, you should be able to find enough available accommodations to choose from. But keep in mind that most deals in Europe (even in hotels) are Saturday-Saturday with six days of skiiing in between (you could include the Saturdays too, if travel plans allow). You can deviate, of course, but availability will be less and places will probably be more expensive if you do. I think that's good to know when choosing an arrival day (if you have the choice)
Here are some Epic Ski trip reports on St. Anton: