The MOST central zones in Old Madrid are Plaza Mayor, Puerta del Sol, & Opera. Just a little
further would be zones of Huertas and Gran Vía.
You're probably looking for 1-2 Star Hotels for a double or any of the hostels (called "hostales" in Spanish - and not to be confused with YOUTH hostels which are called "albergues juveniles"). Regarding the possibility of an apartment, the vast majority of these START at about 100 Euros/night and go up from there but there are some exceptions.
Be sure to browse the following directories of links to websites (their locations are included below the link):Madrid Hostels
@ http://www.MadridMan.com/madridhostels.html Madrid Hotels
@ http://www.MadridMan.com/madridhotels.html Madrid Apartments
First, find some that look nice in an area in which you'd like to stay. Then, with that name in mind, come back here to this category and conduct a SEARCH to see if there are any reviews.
You'll find a lot more information about Madrid & San Sebastián-Donostia in the pages of MadridMan.com as well as in the "Favorite Places" category of this message board. Just browse or conduct a search to find those previously posted threads. If you find nothing that answers your questions, post a new one with specific questions. Many people, including me, find it difficult (and laborious) answering the general questions like "Could you tell me what to do while in Madrid" or "Could you tell me where to stay while in Barcelona?" as examples. The more specific your questions the more likely you'll get answers.
Have a wonderful time in active Madrid, Elegant San Sebastián-Donostia, and the somewhat interesting Biarritz, France.
for Barcelona information, Transportation, Lodging, & much MUCH more!
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