The royal palace of Madrid, Spain is located at the city center with a nice park next to it and a vast garden underneath. It is still today the official seat of the royal family of Spain but they actually live in the Palacio de la Zarzuela a little bit outside of the city. The Palacio Real was first used in 1764 by king Charles III. It is a very large palace with 2000 rooms and is double as large as the Buckingham Palace.
Before the Palacio Real was built there was a castle of the moors on this site – an Alcázar. It was used by the Spanish kings but burned down in 1734. Within the current palace you can find interesting collections of artworks and weaponry. You can book a timeslot for a visit online. As it is directly next to the palace you might also consider a visit to the Cathedral de Santa María de la Almudena.
Calle de Bailén, s/n