Kasuga Taisha, a UNESCO World Heritage site, is a famous Shinto shrine in Nara. The Kasuga Grand Shrine is most famous for the the stone and bronze lanterns (well into the thousands) that can be found all around the shrine. It is at the far end (northeast I think) of Nara Park but is worth the walk, which is probably about 20-25 minutes from Todaiji. According to The Yamasa Institute:
Kasuga Taisha Shrine is one of the most important Shinto shrines in Nara and is one of the “Three Great Shrines” of Japan. It was officialy established in 768 by the Fujiwara clan, but is believed to date from the beginning of the Nara period (710). The shrine is located at the western foot of Mt. Mikasa and Mt. Kasuga, sacred mountians from which the Shinto kami (gods) first descended. The powerful Fujiwara clan (one of the most powerful aristocratic families of the period) and the Imperial court worshipped here, making it very prosperous. Kasuga Taisha Shrine was unified with Kofukuji Temple in the later half of the Heian period (794-1185) with the emergance of the new theological philosophy of Kami-Buddha Fusion. The Shrine’s affiliation with Kofukuji lasted until the Meiji restoration (1868-1912) when the government established Shinto as the state religion and ordered the separation of Buddhism and Shintoism.
If I had to pick a time of the year to go, I would try to go when they have festivals and light the lanterns. They do it only twice during the year, once at the beginning of February and the second time during the Obon season in the middle of August.
Of course going anywhere in Japan during the fall is not a bad idea. Also, apparently there is a really nice botanical garden with over 300 different kinds of flowers/plants. The garden is most famous for Wisteria which bloom from around the middle of April to the middle of May. Also Camellia flowers can be seen from early February to early April and Japanese Andromeda from late February to the middle of March.
