This museum is highly recommended for those with an interest in the history of the Japanese people. The objects on display come from various archaeological sites in the area, including several kofun . Although most explanations are in Japanese, there's enough English to give you a general flavour. To get the most out of the museum, bring a Japanese friend to explain things. Foreigners can enter free (bring your passport).
From Kashihara-jingū, walk out of the northern gate of the shrine (to your left when you stand with your back to the main hall), follow the wooded avenue for five minutes, cross the main road, continue for 100m and turn left at the first intersection. It's on the left soon after this turn.