I have a few a few days in MADRID AND SEVILLE later this month. Besides art I am looking for markets and other experiences that are less touristy. Traveling solo.
I can't say about markets, but if you are an art lover, don't miss the Prado in Madrid.
Also, take day trips to Toledo and Segovia.
Seville has so much to see and do, check out TripAdvisor under things to do in Seville. Don't miss the cathedral where Christopher Columbus is buried.
I'm a big fan of some of Madrid's smaller museums, most of which are at least a step off of the tourist paths, getting you into neighborhoods: Sorolla Museum, The Cerralbo, the Palace of Liria, the Lazaro Galdiano, to name a few.
In Madrid, the Thyssen-Bornemisza Museum is one to visit. It was a private collection of masters, now on public display. Also don’t miss the Museo Reina Sofia where Picasso’s “Guernica”is on display.
Sevilla- the Alcazar, the Royal Palace should be visited along with the Sevilla Cathedral and the Giralda Tower., the former minaret of the mosque which was where the Cathedral was constructed. As mentioned above, Christopher Columbus’ tomb is in the Cathedral.
We also visited the Bull Ring, not during any bull fights! It was rather interesting to see.
There is a ceramics museum in Sevilla in Triana. We really wanted to go but it was closed the day we had time.
I really liked the Reina Sofía Museum in Madrid - 20th century art, largely Spanish, including Picasso’s Guernica.
For Madrid you might be interested in El Rastro flea market if you’re there on a Sunday. Just beware of pickpockets since it can get pretty crowded.
Edited: If you’re a Goya fan, visit Hermitage of Saint Anthony of La Florida. It contains frescos by him as well as his tomb. It isn’t very large and doesn’t take long to see.
Great suggestions up thread. We loved the museums, markets and exploring the neighborhoods. Our favorite Mediterranean restaurant is in the Huertes. We were there several years ago and it was “a less touristy experience.” A full dinner was very reasonable. We ate their twice. We walked there from Puerto del Sol. Enjoy your stay! https://www.thecrazytourist.com/best-things-madrid-spain/
Edited to add: Restaurant- https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwjz1tma-vv5AhUWHzQIHcYyDmIQFnoECDcQAQ&url=https%3A%2F%2Ffoursquare.com%2Fv%2Fla-sanabresa%2F4be2b9691dd22d7fb69e94bd&usg=AOvVaw3UOONgbiPNzYLkOcbJ0cnJ