四天王寺
One of the oldest temples in Japan — founded in 593 by Prince Shotoku, predating most of Kyoto's big names by a century. It's a quieter visit than the Dotonbori-side shrines, which is part of the appeal: a big stone-paved compound in the middle of the city where you can actually hear yourself think.
Pair with Abeno Harukas — both are in Tennoji.