Go to the Buddhist Stupa in Bodha, northeast from Kathmandu centre. It's a bit difficult to find, due to Nepal's lack of street signs, but once you're there it's a fantastic spot to watch Buddhist monks go about their usual business and just to contemplate life and the world in general. There's also a great restaurant run by an Italian lady where you can get a huge plate of vegetable chowmein for 15 Nepali Rupees, approximately 8 pence.
Northeast of Kathmandu town centre