Over the last several years, Madrid's river redevelopment has really come together. What used to be sludgy is now sparkling, with walkways and bridges intertwined along the river, with kids playing, people jogging and chatting. A great place to get away from the crowds, even in the winter. Tourists don't really know about it, which makes it even better.
Go at sunset so you can watch the lights of the city come on and the moon rise. Start on the south side, by the new Matedero arts center and move your way up north to the Royal Palace. Delightful way to spend an early evening.