Per recommendation from Arturo, we tried to go see the Royal Palace of Aranjuez. Sadly, when we arrived, it was closed without notice, so we only got to see the gardens. Sigh, mostly wasted time (2H going there and back, and 2H onsite...)

We took a morning local train:

It was a 10mn walk from the train station, and we only got to see the gardens, which thankfully were still ok: