If you're eager to inject a little more culture into your trip, put Kashihara Insectarium on your list. Check if guided tours are available or just wander around in your own time.
You'll be spoiled for sightseeing choice when staying in Kashihara. Kashihara Insectarium is a great place to kick off here, but there are plenty of other worthwhile sights to consider. Kashihara Shrine, Ōmiwa Shrine, and Hase-dera Temple are not far from the museum and will fill in your day nicely.