Probably the first place to start in a cultural tour of Tainan, the Confucius Temple (and it is indeed, the "Confucius" Temple, not the "Confucian" Temple) is located a little less than a kilometer away from the Tainan railroad station.
Its status as a "temple" may not quite fit the definition that Westerners have of a temple. It is not a single building, and is more of a museum that a conventionally sacred site. In fact, it includes a shrine to the God of Literature, together with an inscription pointing out that Confucius would have disapproved of such superstition.
Along with that temple, the grounds also include the old school building, as well as the central pavillion where ceremonies were conducted, which now includes a collection of musical instruments, names of famous scholars, and other antiques of Confucian culture. Outside is a shady yard and a fountain.
The temple was established as part of Cheng Gong's efforts to preserve the culture of China on Taiwan after the Manchus had taken the mainland. Many of the buildings date to that period, and their is still faded stone inscriptions and bas reliefs from that time.
Since the temple is mostly free, with only the inner building costing a slight 25 NT to enter, it is probably a good place to visit for those visiting Tainan.