Piemonte has a large variety of places in the mountains where you can stay outdoors to do some sports. Most of all, the Alps.
I suggest you, if you come to my region, to go to the Gran Paradiso National Park, that is between the regions of Piedmont and Valle d'Aosta. There are many paths for any levels of hiking: here you'll find beautiful landscapes, lakes and animals like ibex and marmots. This is a little corner of peace in the middle of the Alps: now you are on top of the Gran Paradiso. Such a big paradise!
Photo Credits: Silvia Cartotto
Another place to go and trek is Valpelline, a valley in the near region of Valle d'Aosta. On the way from the village of Dues to the one of Ollomont you'll find some nice paths suitable also for those who want to do other sports, as go by bicycle or climbing. The view around you is just amazing...
Photo Credits: Silvia Cartotto
Do you need other ideas? Let's go to the Toce Waterfalls, in the north of Piedmont! The walk to the top is not so long and also suitable for beginners. Once there you can go on following the road: lakes, small villages, sweet trails go up to the mountain.
Photo Credits: Silvia Cartotto
Finally, did you know that Chamois is the only village in Italy that is not attainable by car? Yes, we are in Valle d'Aosta and this small village is reachable only by the cableway or by foot or by bicycle: so is perfect for a sporty tourist like you. I suggest you to go till there from the near village of La Madeleine.
Photo Credits: Silvia Cartotto
At the mountains, most of all in Piedmont, there is always a sport that you can do: go by bicycle, climbing, running, trekking, hiking or just walking... you have free choice! But remember: the best thing you can do, after some days in the midst of nature, is to stop and admire it. Just wonderful!