Nako Monastery
Allegedly founded by Ringchen Zangpo in 996 AD. A complex of small old temples with fine old sculptures and frescoes, sadly some of them neglected. There's also a new temple built in recent years.
day walks
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.
Gates in the village streets
Built from stone and wood and painted in the inside with colourful Buddhist religious paintings.