Madrid is the ultimate foodie getaway. A food tour is a must-do. There are many operators listed in Viator offering gastronomic tours of Madrid. I just counted 23 tours. You can sign up for any of those tours except the ones that offer Flamenco dinner experience. I do not recommend having your dinner in a flamenco tablao. The best tours are the ones that focus on restaurants in the historic center of Madrid.
I have been on tapas tour organised by Devour food tours. I have no hesitation in recommending them.
Go on a food tour on your first day at Madrid. That way, you will then be able to decide on where to go, what to eat and also learn about touristy restaurants that you should avoid.
The Paseo del Arte (Art Walk) is one of Madrid's iconic avenues housing three great Museums - The Prado, Thyssen-Bornemisza and Reina Sofía museum. Together they represent one of world's best collection of art works, from the Middle Ages to modern era. The Art Walk is an essential part of Madrid experience.
Buy the Paseo del Arte ticket which includes one visit to the permanent collections of each of the three museums comes with a 20% discount on the admission prices.
To make the most of your Art Walk, download the official Essential Art Walk App
Madrid is a compact city made for walking. Sign up for a free walking tour of Madrid organized by Sandemans.
I also suggest their night pub tour. They take you to different districts every night. Avoid the days when the tour is to touristy Plaza Mayor. Sign up for their Sundays and Mondays, for their tour of Huertas neighborhood.
You should go on a DIY tour of Mercado de San Miguel. In the market, you will find stalls selling all kinds of tapas, Jamón, wine, Iberian ham, cheese, oysters and other local delicacies. You can try them all without the need to go outdoors. Market also has bars serving local vermouth on tap.
Tours by Spanish Sites are really unique. They are all well researched and organized under the guidance of David Mathieson, who has written extensively about politics and Spain in leading publications including the Guardian and Financial Times.
The tour on Spanish Civil War is highly recommended.