Dujiangyan Old City is not ancient in the untouched sense; much of what you see has been rebuilt or restored, especially after earthquake damage. Still, it is a pleasant and logical extension of a visit to the irrigation system, with gates, old-style shopfronts, bridges, and streets arranged for strolling.
Treat it as atmosphere rather than archaeology. After the engineering brilliance of the UNESCO-listed irrigation works, the old city gives you somewhere to decompress, eat, and watch how a major heritage destination turns itself into a full-day town experience.