Matsue is famous for wagashi, traditional Japanese sweets. Saiundo will demonstrate the making of traditional Japanese sweets, and you can receive one each.
If you are interested in buying omiyage, local specialty gifts to take back with you, their shop is close to the venue.
https://www.saiundo.co.jp
Google Map link: https://goo.gl/maps/764Lz7Z9hJXgsAty5

Senchasou will serve tea and coffee. They also have a nearby shop.
https://www.senchasou.com
Google Map link to Kiyomise original store: https://goo.gl/maps/nUN9sVSAXzGsTK4r7
Google Map link to Ichibata Department Store (B1 tea corner): https://goo.gl/maps/VtEaR54Cgm2it2Zf6