Photo: 663highland, CC BY 2.5 via Wikimedia Commons
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.
The Nara National Museum is one of the pre-eminent national art museums in Japan.
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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).
吉城園
Really nice garden that is worth a visit because it is free. Can be coupled with the Isui-en Garden as the entrances are right beside each other.
依水園
Enjoy the magnificently arranged garden with full of flowers, surrounded by all the rest of Nara Park. Restaurant on site.
興福寺
This temple has a three-story and a five-story pagoda; historically, the latter has contended with Kyoto's Toji for the title of Tallest Pagoda in Japan, although Kofuku-ji seems to have surrendered for now.
浮見堂
A hexagonal building built on Sagiike Pond in Nara Park so that it appears to float on water.
猿沢の池
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.