Kallanai is an ancient stone dam across the Kaveri, about a short drive from Trichy. It is not monumental in the way a temple tower is monumental; its power lies in the fact that a low, practical structure changed the agriculture of the delta for nearly two thousand years.
Come for the river setting and the engineering story. It pairs naturally with Thanjavur or the Kaveri temple circuit, especially if you want to understand why this flat green region became so prosperous under the Cholas.