I would not stress too much about it. I recently moved to Switzerland, and if you come from flat greenish countryside, then anywhere mountainous will make a nice change. And the other thing is that the Alps are not all that deep, so 3 hours very brisk driving gets you from Zurich (not really alps) to the Stelvio (dolomites).
Where to go depends on what you want to do and how far you want to drive.
If you want to tick off some classic road passes then somewhere like Interlaken might be nice. Or to ride on some roads which are absolutely beautiful but not heard of by anyone and do less driving you might stick with the Black Forest. Somewhere in between is Central Switzerland. If the latter you could stay somewhere like Einsiedeln, which gives you watersport options for the family, flat roads round the Sihlsee or other lakes plus lots of climbs ranging from the Pragelpass, Ibergeregg, Sattelegg which offer 10km at 10% or so, or you can ride up the Rigi if you wish to emulate recent Vuelta stages.
Check out http://www.quaeldich.de/
for ideas on climbs in each location - there is a map function there with all the passes / climbs in the locality highlighted. Very easy to make up leg-breaking rides that way