Hey Noogie,
Sorry but I can't help you with the climbing... my fear of heights stops me with that!
But as for the snowboarding, pretty much every resort has a snowboard school. You can just decide where you like to go and then check out the school there. If you are going to head away for a few days it leaves more options open to you. Traveling back and forward from Davos, Laax or Lenzerheide can be a bit tedious, even though thats what I normally do myself. If you do decide to go this route I can recommend the Primus school in Lenzerheide. I took a one off lesson there once and they were really good.
If you are looking for somewhere that is easy day trip distance from Zurich then most people here on the forum will probably recommend Flumserberg to go and learn. Personally I find it very cold (sun only really shines on one piste), and the lines at the lift can be horribly long. I learned from scratch in Hoch-ybrig,and despite one or two anxious moments on the first day it worked quite well.
You can check out the website myswitzerland.com for
snow reports, they allow you to select the resort by region and it gives you information about the resort as well as a link to their website.
If you have anymore questions just ask.