|a walk along the river|
If you don't want to go in the palace, the 300 hectares of gardens offer a nice stroll (flowers blooming even in October). They're so nice they inspired composer Joaquin Rodrigo to write the Concierto de Aranjuez for Spanish classical guitar and orchestra.
If food is more your thing, the restaurants in town are well-known for their fabulous produce. Asparagus and strawberries are the most famous crops from this area and are sure to be on your menu del dia. There's even a steam train, originally for transporting the Royals and also produce to the capital, that operates in summer on which passengers can do a "strawberry tasting".
It's called.... The Strawberry Train.