Known to most locals as “Mt. Kurotani” (黒谷山), Konkai Kōmyō-ji is one of the head temples of Jōdō branch Buddhism. It was founded in the late twelfth century, and lies on a hill between Mt. Yoshida to the west and the Higashiyama range to the east. The temple has a comparably large cemetery, which alone invites interested visitors to explore the graves of several historical personalities, among them the Martyrs of Aizu, who were defending the Shogunate during the early Meiji restauration until the bitter end.
The current temple buildings are rather new, having been built in 1942. While the main hall is open to visitors year-round, a wet-landscape style strolling garden only opens sporadically, usually during the spring and autumn seasons. From the square in front of the main hall, one can enjoy an overlook towards the city, and also peek into the Amida Hall. On top of the cemetery stands a pagoda which is designated as a national treasure.
Since the temple grounds are located next to Shinnyo-dō, I would explore the temple on a little stroll from Mt. Yoshida to Shinnyo-dō and perhaps further towards the Philosopher’s Walk.

Admission: temple ground open year-round, gardens opening in early summer/autumn
Nearby places of interest: Shinnyō-dō, Eishō-in, Yoshida Shrine, Takenaka Inari