Madrid, first of all, is a great walking city. If you are staying anywhere near the Puerta del Sol. you’ll perhaps first notice that Madrid got smart several years ago and banned all car traffic in the Puerta itself as well as all streets leading out of it for a distance of several blocks. Usually the only vehicle you’ll ever have to contend with is the occasional taxi that has received dispensation to come into the center to drop passengers at the hotels.
Spaniards love to walk. They do it all the time, but particularly in the early evenings and Sundays when they habitually dar un paseo with their girlfriends, or their extended families, or whomever. They don’t necessarily have any destination in mind, except perhaps a restaurant or bar. They just like to walk.