It sounds as if you will be in Spain on May 18, Museum Day, when at least some museums will be free. Here's a Trip Advisor Thread about that day. Some quick Googling didn't turn up an independent website listing the participating museums, but perhaps the information will be easily found as we get closer to the date.
I stumbled on Museum Day during a visit to Madrid in 2016. That year it fell on a Wednesday, whereas this year it's a Friday. That may affect visitor traffic. I suspect the free-entry situation was not widely known in 2016, because I went to the Prado, of all places, and it wasn't excessively crowded. If I hadn't had that experience, I'd have definitely said, "Avoid the Prado on May 18." As it stands, I really don't know what advice to give. A conservative traveler might opt to try the Reina Sofia or the Thyssen that day. Or perhaps there will be a bunch of smaller or less popular museums also participating. The Royal Palace seemed to me extremely popular with Spaniards, who are perhaps more knowledgeable than foreign travelers about Museum Day. (It's probably mentioned in the local newspapers, too.)
The Monasterio de las Descalzas Reales was free for me in 2016. I enjoyed my visit a lot, but I was unsuccessful in connecting with an English-language tour. Unless their procedures have changed, non-Spanish speakers should read through Rick's description of the convent at least twice before visiting.
