Tōshōdai-ji was established in 759 by influential Chinese priest Ganjin (Jian Zhen), recruited by Emperor Shōmu to reform Buddhism in Japan. The main building, the Kondō (Golden Hall), dates from the 8th century and houses an impressive 5m-tall Thousand-armed (possibly literally) Kannon (Buddhist goddess of mercy), among other National Treasures. Behind it, the Kōdō (Lecture Hall), also built in the 8th century, was actually originally part of Nara's Imperial Palace – today it's all that remains of it.
By train, take the Kintetsu Nara line to Yamato-Saidaiji Station and transfer to the Kintetsu Kashihara line for Nishinokyō Station. The temple is about 500m north.