It’s an easy hop over from New York—in fact I just made the trip last night. Greetings from Madrid! January maybe isn’t the best time, but cheap flights could easily compensate and 5-6 days is about the right length for a good visit with maybe a day trip in there. With not a whole lot going on
Madrid is on about the same latitude as NYC, so daylight is about the same, but Spain’s displaced time-zone means sunrise and sunset are notably later. Historically, Madrid should be just a bit warmer than New York, but historic norms are out the window for both places (all places?), and the this winter the weather is more similar (and warmer than normal for both.)
The hotel Mary mentions above is in a great location—it’s the general area I always recommend. But the center is fairly compact and all very walkable, so it’s hard to go wrong.