Graubunden is the largest canton, the name for a swiss state, and is the southern and most eastern part of Switzerland. It borders Italy in the south and east and Austria in the north.
Most of the highest and most spectacular peaks of this area create the borders with the neighboring countries of Italy and Austria. So getting closest to the borders is the best. Flying into Milan or Zurich are the closest international airports, and from there just hop on a train.
Hiking, mountain biking, and mountaineering are a few of the outdoor options in this nature-lovers paradise. And depending on what type of excursions you want to do the list could be endless. There are guided glacier walks for less experienced folks who want some icy adventure. The high peaks in the area are great for real mountain climbers who want to ascend to the top. There are many well-marked hiking trails that lead from quaint towns to mountain huts and hotels. Mountain bikers also take advantage of the well-marked paths.
For adventurous hikers who want to stay in the mountains, the area offers many well placed mountain huts for overnighting. The huts are clean and offer dorm-style beds called Matrazenlager and breakfast and dinner in the halbpension option. A famous hut-to-hut hike is called the Bernina-trek. It is a seven day hike starting in Madulain and ending in Poschiavo, staying in the huts Es-Cha, Jenatsch, Coaz, Tschierva, Boval, and Sao Seo. Beautiful glaciers and peaks can be seen bordering Italy here including the Piz Bernina, Piz Roseg, and Piz Palu.
Being a member has the advantage of 10 or so Swiss Francs (CHF) off per night at each hut (57 CHF vs. 66 CHF for non-members). So if you are staying in the huts for over a week then being a member is advantageous. In addition if you are already a member of another regional alpine association such as the Austrian or German then you get the same discount.
Switzerland is not part of the European Union and does not use Euros, it uses Swiss Francs. Euros however can be used in certain places but the exchange rate might not be that good. Swiss Francs are easy to get from ATM's at the airport or regional banks. Swiss people speak Swiss-German, a dialect of German, French, Italian and Romansch. Graubunden is home to Romansch speakers, but most also speak German, Italian, and sometimes English.
For more info on this hike click here.