We had a pleasant, short-break at the Hotel Wellington in Madrid a couple of years back. It was a little bit old fashioned, but very clean, with nice rooms (though the view to the rear wasn't too pleasant). It is in a nice area, with lots of upmarket boutiques etc in the surrounding streets.
We stayed in the Wellington a couple off weeks ago. It's a little bit like the Shelbourne without the atmosphere, but still quite nice. It is very central and is within walking distance, or very short taxi ride of most major sights and shopping. We booked it because it was the only one we could find with an outdoor pool. It's very quiet, but it's a good base to see the city from.