There are some nice day walks around the mountains if you're reasonably fit. Behind the lake you can head up the mountain towards the visible chortens which is a nice viewpoint. If you still have a lot more energy continue around to the other side of the range for views east towards Tibet. In 3 to 4 hours you can reach the village of Tashigang perched high above the Sutlej valley, with an interesting temple. The only things you'll encounter underway are sheephearders and great views.