You could live in either Zurich or Geneva and go skiing every weekend.
I live in the village of Champéry (part of the Portes du Soleil ski resort) and work in Lausanne ... and get to ski every weekend in winter and get the most of the summer sports (biking cross-country, downhill, climbing, hiking etc). There are a fair few people in Champéry who even make the daily commute to Geneva, Fribourg and Bern. They love the mountains that much!
The great thing about Switzerland is the transport network. Of course, it is handy to have a good, and reliable car, which we do because of where we live in the mountains, but the trains are very reliable. There is a train from Geneva to Aigle. You would then have to change trains onto the AOMC mountain train which takes you to Champéry. All the main swiss resorts have train connections. Check out the swiss train website (
www.cff.ch), and you work out how long you're willing to travel.
From Zurich, you have Klosters, Davos and St-Moritz; with Geneva having a closer proximity to Champéry, Verbier, Nendaz, Crans Montana, and the ever special Zermatt. Over the border in Italy, there is some good skiing too. Don't forget to check out Saas-Fee, Lenzerheide and Laax. Chamonix is one of the free-riding paradises.
Portes du soleil is special as it is linked to many resorts so you can never get bored. There is also skiing for all levels. There are some great restaurants on the slopes (both swiss and french sides), and some good après ski (if you know where to go). Champéry village has a charm which keeps people coming back. It's not a place to be seen. It's place to ski. It's always recommended to pre-book accommodation to not be disappointed, especially during peak times. If you're planning on skiing every weekend in one resort/ area, you should think about getting a season pass and perhaps about renting something for the season, instead of hotels every weekend. At least you can leave your ski stuff there if you're taking the train. If you're on a strict budget, see about renting with friends. There are currently "early bird" discounts in most resorts, for buying your ski pass.
As you've only had 2 weeks skiing experience, you should think about taking private lessons to get a decent technique base (you'll get a lot further, and quicker, than with group lessons), as opposed to picking up bad habits if you're on your own. Even great skiers need tips...and they take them! You can only improve on your technique.
Wherever you decide to base yourself, you'll be able to find decent skiing. If it's a "bad" looking season (like last season), look at higher altitudes. It'll be cold, but at least they can make the snow.
Good luck and happy skiing.