This is not the largest, but it is arguably the most beautiful of the Royal Palaces, with its exquisite rooms such as the Porcelain Room and the Mudejar adornment of the ceiling in one of the antechambers.
Every single room hold stunning surprises. Many of the ceilings are extraordinary, but the hangings, the decorations, the paintings, the furniture are all beautiful. You never know where to look to see something unexpected.
On Wednesday afternoons there is free entry after 3pm to anyone who can accredit EU citizenship (ID card, passport, etc). The free entry is done as a free-format visit, with no guided tour option. You simply follow the route around the rooms and stare in wonder at the extraordinary art, clocks, porcelain and hangings. The visit takes about an hour if you do it at a gentle pace, looking at everything.
You can hire an audioguide for 4 Euros which will give you many more details of the palace and its decoration.
After finishing, turn left and go through the arches into the gorgeous palace gardens, allowing yourself to wander among the trees, the fountains and the pathways alongside the river. It is a peaceful sanctuary in the middle of the city, with free entry.
Photography is not permitted in the palace, but you should certainly have your camera to hand in the gardens. Even in autumn and winter there is plenty to see and plenty of attractive corners to photograph.