What to do in Madrid on a Sunday in April?

Well, my choice would be the Reina Sofia, to see Picasso's Guernika if nothing else.
Or the Prado for the Goya Black paintings.
Then a walk in the park.
Then I'd sit in a square with drinks and tapas and watch the world go by.

If art is of interest, then you are missing three great museums, with the Prado at the top of the list.

If a nice day, then a stroll around Retiro Park, or the nearby botanical gardens might be nice and relaxing.

If flea markets are your thing, or just like to people watch, the El Rastro market is great, stretches along a street, lots of stuff from clothes to antiques.

An overlooked spot is the Temple of Debod, an Egyptian temple that was gifted to Spain, transplanted and set up in a park setting.

There are also some museums of specific interest, Bullfighting, the Real Madrid soccer stadium and museum, and a naval museum to name a few.

That probably only scratches the surface.

Look at the “things to do” section of Trip Advisor (or other site) to get some ideas based on what you like to do, what wasn’t covered on the tour, where in town your hotel is, and whether you have any mobility issues.

One possibility could be walk through Retiro park, go past Alcalá gate, then walk down Paseo de Recoletos past Fuente de Neptuno, Cibeles Plaza, down to the Rana de Suerte sculpture and Fernando Botero’s Lady with Mirror sculpture.

Another option would be a walk along the Gran Vía and over to the Plaza de España with the statues of Don Quixote and Sancho Panza, then over to the Temple of Debod.

Along either route there are markets that are mainly food halls now that you could go into.

One town close to Madrid that’s easy to reach and worth a day is Alcalá de Henares, Miguel de Cervantes’ birthplace. Assuming the free day is the day prior de departure you may not want to take a day trip and just relax around town.

Hola,
I had the great pleasure of taking the RS "Best of Barcelona & Madrid" nine years ago. The current itinerary states on Day 6 "This morning we'll tour the Reina Sofía, Spain's greatest modern art museum and home of Picasso's Guernica. Then we'll make our way to the masterpiece-packed Prado — where you'll see paintings by Velázquez, Goya, El Greco, and others." Unless policy changes happened, tour groups of both these wonderful museums are limited to 90 minutes. However, your entry ticket can be stamped for re-entry later that same day. Also, the last time I was in Madrid, Reina Sofia was "free" after 13:30 on a Sunday afternoon. If "art museum fatigue" is not an issue for you, just up the street fron Reina Sofia (and nearly across the street from the Prado) is the Thyssen Museum....a more comprehensive collection than either The Prado (no modern art) or Reina Sophia (almost entirely modern art).
If you are a fan of futbol (soccer) Atletico Madrid hosts Athletic Club Bilbao on Sunday April 19 (my two favorite teams in La Liga) and Real Madrid hosts Girona on April 12.

I'd like to also recommend visiting the Thyssen (Museo Nacional Thyssen-Bornemisza) - we spent hours there in October 2025. It's got a wide representation of artistic periods and you will even find one of Edward Hopper's largest paintings - "Hotel Room" from 1931!

My favorite thing to do in Madrid was a walk on Gran Via, looking at those beautiful buildings.

Something you didn't list was Almudena Cathedral. If you like cathedrals, that one is magnificent. It's next to the Royal Palace.