Sounds great.  Heart of the season, should be decent to excellent conditions just about anywhere.  You have one week, that would seem to dictate picking one big place and sticking there.   Many Alpine ski areas want you to pick lodgings for a full week from Sat to Sat or Sun to Sun.  In Europe they have the equivalent of condos or “self-catered” apartments, but also many old fashioned lodges/hotels where some or all meals come with the price.  You have to decide on which approach you want.  Believe Chamonix is only about an hour travel time from Geneva.   Val d’Isere and Les Trois Vallees would be about three hours, Zermatt 2.5 hours.  My only skiing in the Alps was in Austria, which is about twice as far as the others from Geneva and not a logical choice for your scenario.  Speaking only from reputation, Chamonix FR is supposed to be epic, but somewhat disjointed requiring bus rides to the several different ski mtns there.  Meribel is supposed to be a friendly, moderately priced entry point/village for Trois Vallees FR (huge lift-linked ski domain:  ₁₈₀ lifts/370miles of trails).  Val Thorens is the higher elevation base village for Trois Vallees if you wanted the most snowsure location.  Val d’Isere is supposed to be a dang good place for expert skiers and also huge.  Zermatt SZ, which I’ve been to in summer, is incredibly scenic, with perhaps an emphasis on long groomed runs and a beautiful base village.  Portes de Soleil is another large French resort only about 1.5 hours from Geneva, don’t know much about it, except almost as big as Trois Vallees and straddles both FR and SZ.

IMHO this is the best website to research European ski areas:  http://www.wheretoskiandsnowboard.com/

Here is their page on Val d’Isere, which my gut tells me is a top one you should consider:  http://www.wheretoskiandsnowboard.com/resorts/valdisere/

They also put out a fine hardcopy guidebook under same where to ski and snowboard name that I’ve found in a couple of my local public libraries.PS:  you better post some post trip pictures or I will be pissed :-)