The Roman Theater of Ascoli Piceno is an archaeological site near Porta Romana, also known as Porta Gemina, on the western edge of the old fortified town. The remains are still being excavated, so the site is more fragmentary than the city's churches and palaces, but it adds an important Roman layer to Ascoli's history.
Pair it with the nearby walls and Porta Romana if you are walking the western side of the historic centre.