Swayambhunath is a Buddhist stupa atop a hill in the Kathmandu valley. It's best to get there before sunrise - you'll be unlikely to meet any other tourists, just crowds of Nepali and Tibetan people. Swayambhu is a hive of activity at this time, with chanting, meditation and worship playing alongside the pre-school karate class, police training up those steep steps, earnest young men doing their exercises, the games of the monkeys and dogs.
It's a wonderful place at any time, but I think you see it at its best and most natural at sunrise. Beautiful light for photography too, if that's your thing. And there's a lovely view across the Kathmandu valley. If you fancy a walk, there's a lovely peaceful monastery at the top of the next hill along.
It's an easy walk from the centre, but you could also take a bus from Sohrakhutte, or find a taxi. Ask to be dropped at the bottom of the steps, rather than at the top. Then walk up to the stupa
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