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This small pond at the east end of Sanjō-dōri with Nara Park behind or Naramachi to its south is a very popular viewing spot for Kōfukuji.
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Learn basic Japanese calligraphy or origami. They'll pick out kanji that match the sound of your name so you can learn to write them with a calligraphy brush pen. Or you can learn to make an origami deer, something you're not likely to find outside of Nara. The teachers are charming, and the center has other cultural activities as well, and all the other information you'd expect from a visitor center.
A little gallery with photos of traditional Japanese tattoos, run by a tattoo artist who will talk to visitors about the difficult social and legal status of tattoos in modern Japan.
元興寺
It was considered to be one of the seven most important temples in Nara when Nara was the nation's capital. The original temple burned down in the 18th century, but the architectural style remains true to the original, with its unique Korean-style roof. The mandala within the temple is one of the most famous in the nation. Around the outside of the temple there are many Buddhist statues, but perhaps more interesting are the various demon statues scattered about among them. While the Buddhist statues are quite typical and obviously religious, the demon statues are comical and seem out-of-place. Some even appear sacrilegious, with a demon doing Zen meditation among the Buddhist statues and another in a rather erotic centerfold-like pose. There is a story that supposedly associates the demons with the temple. For visitors, it is fun to try to spot them all.
奈良国立博物館
This museum has one of the world's best collections of Buddhist art and changing exhibitions. The National Treasure Hall has an impressive collection of statues. There are "English Guides" inside the museum however, they do not guide you through the museum; instead they are there to answer questions. The guides are highly knowledgeable, so if you can think of questions that require explanation, you can learn a lot more about the exhibits, Buddhism, and Buddhist art. Each year for about 2 weeks in late October - early November (dates vary) the museum hosts on a rotating basis a part of the collection of Shōsōin, the Tōdai-ji treasury (which is closed to the public). Expect enormous queues, as this is a notable event in the cultural calendar of the country, and tourists from all over Japan converge on Nara at this time.
氷室神社 Himuro Jinja
A shrine dating from 1217 and home to several fine cherry trees. Although the architecture is unremarkable, the trees in front of the shrine explode into beautiful clouds of pale pink and white blossoms in spring (late March-early April).