Palacio Real Madrid

If i remember we spent something like 90-120 minutes total, and bought our tickets ahead of time. We arrived at opening. The line was much longer when we got out.
The cathedral didn’t cut it for us. Yes it’s big but we all felt outside was more impressive then inside.
I believe gardens are free but we didn’t go

The Cathedral Santa Maria la real de la Almudena is technically free, but it asks for a €1 donation. The gardens of Sabitini are free and one does not have to go into the Royal Palace to get to them. While I haven’t been inside the palace for years, the way it appeared when I was last there in 2017 is you needed a ticket to get into the palace, its plaza, armory, etc.

I went to the Palacio Real in March and as I recall I was able to get tickets pretty quickly as early March is not peak season. I believe I toured everything in an hour or less but that was because I'm not into High Rococo/Baroque style and if I saw one more gilded cherub I would scream. My advice would be if you haven't seen any other European palaces to look inside but if you've been to others, it's a bit underwhelming especially as the Royal family doesn't live there-just uses it for ceremonies.

The cathedral and gardens are both free.

I'm another who regrets the time spent inside the Palacio Real, but in truth I don't care for most palaces at all, so I'm not a fair judge. Let's just say this one was very near the bottom of my list. It did seem very popular; many of the visitors seemed to be Spaniards.

I enjoyed spending an hour or two in the Botanical Garden on my 2016 visit to Madrid. It's quite near Atocha Station. I think the entry fee was 5 euros at the time.

I decided not to visit the Palace, primarily because it's too new for my taste. I'm not really a palace person anyway. I did go to the Cathedral but was completely underwhelmed, again because it has no history. There are far superior churches to visit all over Spain. The cathedral is free. I didn't wander those gardens but believe they are free. I did like Temple Debod in another garden a short walk from the Palace. It's a very old Egyptian temple that was given to Spain for their help with the Aswan Dam.

I checked recently, and it looks as if the interior of the Temple Debod is still closed. I believe you can walk around the outside of it, though.

I was there Nov 2017 on Madrid's feast day, so though I went by the Cathedral to see all the flowers and did see the processions, I didn't bother trying to get into the Cathedral. If I recall, the Jardines are a steep climb down from the Palace. There is a public staircase that leads up to the grounds near the Armory Museum. I wasn't underwhelmed by the Palace, and thought the Armory (particularly the horse plate) was interesting - but then, I haven't seen many palaces. You could consider the Botanical Gardens and one of the numerous art museums near Atocha train stations. Weather might dictate how much inside or outside activities can be done.

We enjoyed the Palacio Real very much, and I do recommend seeing it. I believe it is considered one of the top 3 palaces in Europe. The other two are Versailles just outside of Paris and Schonbrunn in Vienna. Versailles is more impressive and more beautiful than Palacio Real, but I still think it is worth visiting. We rented audioguides, and I believe we spent about 1.5 hours there. My husband and our friend visited the Armory Museum, which they enjoyed a lot, too.

As someone else may have suggested, since you have limited time in Madrid, and if you like art, I highly recommend the Prado and the Reina Sofia if you think you might like that better than the Palacio Real.