One of the most famous places to try out one of its Matcha dango desserts as well as that cake-looking thing with adzuki beans on top which is called "Minadzuki" - a specialty dessert of the Kansai region. I bought the smallest set in a box to try it out at home and it turned out really good, but please note that it is not as sweet as Western desserts.

I would advise buying a small box to try it out at your hotel / Airbnb (unfortunately, I was told that it has to be eaten in 3 days so you probably won't be able to bring it back to your home country) or you could eat those (set N4 on their menu includes a cup of tea, 1 dango, and 1 piece of Minadzuki) right inside the store, which would be perfect if you have never tried those.