Chamonix is in the French Alps and is south of Lake Geneva, so going further east to Zermatt could be somewhat redundant in terms of getting a similar kind of ski resort village experience, not to mention come December could be difficult to get decent accommodations this late in the game.
Traveling north up beyond Lake Geneva into the heart of the Swiss Alps (Lauterbrunnen Valley) would be a quite a long train ride and again, could be difficult to find accommodations available within the valley itself (Wengen, Murren), although many more choices outside the valley (Interlaken, Grindelwald). That said, the scenery, hiking, etc. in the Lauterbrunnen Valley is truly astounding. If you’ve been to Yosemite, think about that experience, then multiply x5, so could be worth the effort, but the travel/accommodation logistics would have to be carefully considered.
For a more urban experience, Lucerne is an incredibly charming city but probably too far north. Closer to Lake Geneva is the capitol city of Bern which also has its charms and would be good for a day trip or overnight.
The easiest choice and still a good one from Chamonix would be to swing up around the east side of Lake Geneva to Montreux which is an historic lakeside resort destination with great old European hotels right on the lake, the famous Chateau of Chillon castle, a long flower lined promenade along the lake, and a warm micro-climate. A great day trip from Montreux is to take the “Chocolate Train” to Gruyeres (cheese, castle, great local wine) and onto the Cailler chocolate factory in Broc (unlimited free samples!), then return to Montreux. If they do this, insist that they bring you back a sleve of this dark chocolate
http://www.cailler.ch/en/sor/fri/noire20.asp
or this chocolate with that has the thinnest layer of hazelnut and cocoa in the middle. Oh my.
http://www.cailler.ch/en/sor/fri/noisette.asp
All of the above assumes flying into and out of Geneva. We flew into Geneva and out of Zurich which enabled us to traverse Switzerland going one way. Some photos from the places named from our trip:
http://picasaweb.google.com/jmackq/Switzerland#