There is no shortage of bars and cafes near you.
For breakfast, we can recommend El Camarote (turn left out of the apartment and walk 50 metres. It is the one just after La Muralla.)
Alternatively, there is a closer one, Pastora, a bit more upmarket (turn right out of the apartment and walk 20 metres).
For bars, our favourite local is La Trastienda, which does nice jamon con tomate tapas. Turn right out of the apartment, walk down to the roundabout, cross and walk 50 metres along Travesia de las Vistillas. It’s on the corner.
For sports bars, the nearest is The Newbridge Irish Bar. If the Newbridge is full (say, for Six Nations rugby), try the Cavern, which is a further ten-minute walk. For the widest range of sports, including AFL, Scottish Premiership and Heineken Cup, you need the James Joyce pub, which is a twenty-five minute walk.