This museum and research centre is an important visit for students of ancient Japanese history. Artefacts come from various archaeological sites in the area, including several kofun, and date as far back as the Jōmon period (10,000 years ago). Foreign visitors can enter for free (bring your passport); you'll get a glossy pamphlet in English that explains the exhibits. It takes about an hour to see everything.
The museum is a five-minute walk west of Unebi Goryō-mae Station, one stop before Kashihara-jingū-mae on the Kintetsu Kashihara line.
Alternatively, from Kashihara-jingū shrine, exit the north gate (to your left 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.