Tengboche Monastery, Nepal
Recently restored due to a fire, it has a quiet vibrancy. The stories of Budha along the main prayer halls should be lingered over, that's if you can handle your feet trying into ice cubes! Like every other Buddhist temple, you have to take your shoes off to enter. Monks readily answer questions, enjoy having a short chat and these sweet men don't seem to mind having their picture taken - ladies keep your hands off since they aren't allowed to be touched by women.
One special place on the trek is Tengboche.
Beautiful monastery set amongst the mountains. You can do a tour of the monastery as well.