Central Madrid is very nice to walk around, I had quite a great time hobbitting around while I lived there, even late at night.
The area near La Latina and Embajadores is nice, has some narrow streets filled with life, including Calle Ribera de Curtidores, where Fotocasion (biggest photography shop in Madrid) is. On Sundays it's in this area that the huge flea market, El Rastro, happens. very worth paying a visit.
I used to walk a lot between Plaza de Oriente, Argüelles (where I lived), Retiro and Atocha. it's a big area but it's full of interesting things. At night the area around Tribunal is really interesting to shoot at, tons of young people partying in the streets and plazas, also it's a nightclub/bar area. this area is called Malasaña.