Your tour continues on the first floor of the Royal Palace with King Charles III's apartment that has four rooms with well-preserved and original eighteenth-century furnishings. The parlor and waiting room have two ceiling paintings by Anton Raphael Mengs, a painter of German origin who was trained in Rome. He was a cultured and strict early exponent of neoclassicism who directly contrasts the bizarre rococo imagination of Tiepolo. You'll also see Roman marble busts and portraits by Goya before finally reaching the king's bedroom.
These halls have a multitude of interesting things to see: after the beautiful Hall of Porcelain covered with tiles from the royal factories, you'll find the sumptuous Gala Dining Hall decorated with 16th-century tapestries on the walls and important frescoes on the ceiling. In two neighboring rooms you'll be amazed by the collections of silverware and ceramic and porcelain pottery, including rich 18th and 19th century china services. You should definitely see the so called "Landscapes Service" which has more than 600 pieces, each of which bears a different landscape from the others!
Before you go through the hall that leads to the exit, make sure to visit the Royal Chapel, which was one of the first rooms built in the palace. It is covered by a dome and decorated with black marble columns and frescoes. A painting above the main alter is by Francisco Bayeu, who will later become Goya's father-in-law. The chapel also offers the chance to browse a large collection of legendary Stradivarius string instruments.
Now that your tour is almost over, you may have noticed that there aren't that many important paintings in the Royal Palace, apart from the eighteenth century frescoes: this is because the most prestigious paintings were all sent to be included in the collections of the Prado Museum. Instead the Royal Palace has maintained its collection of ancient weapons, and I strongly recommend going to see them.
FUN FACT: just in the part of the Royal Palace that you can actually visit, amazingly there are over 600 antique clocks. Imagine the poor court clockmaker who had to wind them up every morning, synchronize them, and fix them when they broke!