The Sabatini Gardens are not one of the main attractions in Madrid, however, it's really likely that you will visit them as they are situated just next to the Royal Palace of Madrid, and, from there, you can take fantastic photos - especially from the entrance that it is closest to the Royal Palace.
(Despite the view of the Royal Palace being in the background, the photos that you can take from the Sabatini Gardens are truly one of a kind. )
The Sabatini Gardens are located in the northern part of the Royal Palace of Madrid (which, in reality, is to its rear). Many people usually think that these gardens are of the same age as the castle, or, like I have heard a couple of times, that the gardens were where the King used to walk around. However, all of this is actually an error, as they only finished construction work on the gardens in 1950.
The project of the Sabatini Gardens was born with the official announcement of a competition organised by Madrid City Council in 1932 to transform the space that was previously occupied by the Royal Stables that Carlos III was sent to build in 1764.
The competition was won by two architects (Anibál Álvarez and Durán Salgado), but the person who finished in second place (Fernando García Mercadal) was actually named as the council architect, and with that power at his disposition, he was sent to construct the Sabatini Gardens - combining his ideas with those of the two men in first place.
I am sure that you will ask about the reason behind this name... well, for a long time, Francisco Sabatini was the Palace architect when Carlos III ruled, and, on many occasions, he planned to have some gardens in the northern wing of the Royal Palace, but the King decided that it was better to build the Royal Stables, which meant that Sabatini never lived to see him dream fulfilled.
A visit to the Gardens will not take you much time, maybe around twenty minutes at best, and you will be able to take lots of photos with the Royal Palace located perfectly in the background. There are lots of sculptures of different shapes and sizes, as well as some fountains. If you find yourself quite tired from walking around the city centre, I recommend that you come down to the gardens and sit down on one of its benches to admire the Palace from another vantage point (especially if it's nighttime).
The Gardens are really well decorated, they are very clean, and all of the bushes are constantly being trimmed.
Price
Entrance to the Sabatini Gardens is completely free.
How do I get there?
If you are coming by metro, it's best to alight in the station, Opera, on the green or red line, and walk in the opposite direction to the Teatro Real. You will see the Royal Palace sideways, and the Sabatini Gardens will start just to the right of it.
If you are coming by bus, you can take lines 25 or 39, which will drop you off just in front of Opera metro station.
The Gardens are located close to the city centre, to Gran Vía, and to Plaza España, so you can visit all of these three aforementioned areas since you're already on the way.