If you take Autostrada Firenze-Siena approaching Siena from the north, you need to find the exit Siena Ovest, looking for Via Esterna Fontebranda, not a big road, but goes straight towards Siena. Before you see the city wall, to your right will be the parking lot Santa Caterina. It is a multilevel underground garage. (See Google satellite map showing the street level).
The escalator is immediately after the city wall to the right. There's an escalator sign with an arrow on the wall (which was how we found it). Escalator is hidden inside one of the open arches within the wall, looking towards the Duomo Tower direction (again check Google street view). There are 6-7 relays of escalators, coming out a block or so behind the Duomo. Remember the location so that you won't get lost finding your way back.