Recomentations for a short travel in spain

Hey, I’ll be in Madrid from June 2 around noon until June 3 at night before my next flight. I’m looking for the best area to stay with good atmosphere, great nightlife, and amazing food especially steak, lamb, grilled meat,. I also want somewhere lively where I can walk around at night, go to bars/rooftops, and experience the city properly. Which area do you recommend and what meat places or nightlife spots should I check out?,