Though I'd describe the distance as more than 3-4 blocks, if I were taking the Cercanias I'd walk from Recoletos to the hotel. Sol is technically closer, but not enough to make sense of changing trains. Heads up that the first 2/3 of the walk is uphill and the sidewalks are narrowish.
Unfortunately, taking the Metro into the center is a three-train, two-change affair. I've done it coming from/going to domestic/western European flights, but I don't subject myself to that ordeal before or after a transatlantic.
To clarify for Jaime, above, the Gran Via Metro station is connected to the Sol Cercanias station by a very long underground tunnel. But there isn't a Gran Via station for Cercanias.
Another heads up: be careful with Pizza Antonia, on the SW corner of the plaza. It's turned my stomach upside down more than once, and I've finally learned my lesson.
You'll be near Entre Santos, wich is one of my favorite restaurants in town. Can be tough to get in.