Here you go:http://www.j2ski.com/ski_resorts/Airports/Basel.html
Some of the best skiing in the world in Switzerland.
If the snow conditions are good you will find many places with pretty tree lined skiing - Villars or Gstaad for example.
If the snow level is higher you may want to look at Verbier, Zermatt or Saas Fee - these are high altitude, glacier fed, big resorts with great skiing for all levels.
We live nr Lausanne and usually take skiing guests for a day at Les Grand Montets in Argentiere (nr Chamonix in France) for the amazing glacier and views but the terrain here is steeper and the best skiing is above the trees. It is only 30 minutes further than Verbier just over the Swiss / French border.
You have many great options. Enjoy your trip!