One of the three Pyu city states (along with Thayekhittaya and Halin), the crumbling ruins of Beikthano are well off the beaten track, but will reward anyone with an interest in Myanmar's ancient history. Of the three ancient states, Beikthano is the oldest (founded around 200 BC). At one point this was likely the capital of the first politically unified state in Myanmar, but today it's little but a few half-hidden walls and raised earthen mounds.
There's a small museum on the site (free entry but you'll need to show your passport), and with luck the museum curator will personally show you around the site.
Beikthano is around 20km west of the small town of Taungdwingyi at around the halfway point between Pyay and Bagan. The site can only really be visited in a private car.