Here's a couple of different suggestions for you.
1. Fly to Zurich, spend a couple of days sight-seeing there (and getting over your jet lag), and then take the train to Arosa for a week of skiing. Arosa is linked with Lenzerheide, so there are plenty of groomers to keep you entertained for an entire week. Also, the town is really nice, the train ride is scenic, and it should be uncrowded in January. http://www.epicski.com/t/95320/photos-from-arosa
2. Fly to Geneva, spend a day or two sight-seeing/getting over jet lag, and then take the train to Les Diablerets. It's another nice town that you get to with a scenic train ride, and it's linked to Villars and Gryon to offer a good amount of terrain. It's fairly low altitude, so it's best to go late-January. But, it's got the Glacier 3000 area about 10 minutes down the road on the free bus, so you're guaranteed to get some snow even in a warm winter. http://www.epicski.com/t/117577/les-diablerets
3. (If you don't mind a bit more crowded and lively resort and you want to visit more towns/cities.) Fly to Zurich and spend a couple of days there, then take the train to St. Anton. It's less quaint and more lively than Arosa or Les Diablerets, but it's still a nice town and offers a huge amount of skiing. After a week there, hop on the train to Innsbruck for a day of sight-seeing. The next day, hop on the train again and make your way to Vienna for another couple of days around town, and then fly home from there. Innsbruck and Vienna are both worth seeing. http://www.epicski.com/t/111201/st-anton-austria-amazing
Edited by CerebralVortex - 9/2/15 at 3:05am