Being our first time in Madrid, we decided we should orient with a walking tour. Chose Letango as recommended by Rick. Jen responded quickly to our request on Thursday early afternoon, and by mid-afternoon we were booked for a Friday morning tour. Gor a great orientation to Madrid, and our guide was excellent. It was a sunny but cool day, so dressing in layers in winter in Madrid is essential. Jen also provided a nice set of restaurant recommendations, and helped us to find a store for something else that we needed. Great support, and a beautiful city for walking.
I recall my Christmas visit to Madrid several decades ago. In addition to the Prado during the day, I found late evening neighborhood bars great fun. You can find bars that cater to regional music, food, and drink. I especially liked one on Atocha that featured music from Galicia with harps and bagpipes, giving evidence of their Gaelic prehistory. You could've been in Ireland, Wales or Scotland. The folks were that friendly.
A walking tour is the best way to get oriented in a new city for sure.