Our time in Madrid was wonderful: the apartment was perfectly located, had everything we needed (including the largest sofa bed I have ever slept in) and was decorated very nicely. Marga was a perfect host, communicating regularly to check everything was alright, and recommending fantastic flamenco nights and hidden treasures in Madrid. We also needed to keep our luggage in the apartment after check-out, as we had a later flight, and this was not a problem at all; which happily meant we could enjoy our last day in Madrid unhampered by suitcases.
The apartment is right by Puerta del Sol, a few minutes walk away from the Gran Via and a short walk away from all the main sights and attractions. It is also very close to a wealth of fantastic restaurants and authentic Spanish bars (where the locals go, not just tourists).
Being so central, however, it is extremely noisy at night, with people talking loudly in the streets until the early morning. But considering where you are, it seems a good idea to embrace the Spanish culture and enjoy the nightlife!