I can't PERSONALLY recommend this place but many others here (and friends of mine) have. It's the
Hotel Europa , located JUST off the Puerta del Sol, on the same side as
Hotel Carlos V . This one has been able to keep its prices down. I think a single is about 53 € and a double is 64 €. It's famous, too! I've heard it described as "funky" by more than one person but you'll find many reviews of it here in this forum if you do a search.
You could also give a hostel a try. Hostels in Spain are called "hostales" in Spanish and "hostals" in Catalán. One shouldn't confused the word "hostels" as meaning YOUTH-hostels though. In Spanish speaking countries, the proper translation for the spanish word "hostal" is the English word "hostel". In the rest of the non-Spanish-speaking world the term "youth-hostels" has been abbreviated to the word "hostels" so you should be careful with this word.
Hostels are family owned and operated "budget hotels" with (usually) simple furnishings, smallish rooms, no/few extra staff-provided services, in-room or shared bathroom facilities, maybe/maybe-not an elevator in the building, but usually very very clean and generally about half (or cheaper) the cost of a hotel.
ANYWAY.... a hostel would be a good and probably cheaper alternative. There are many many hostels in the same area or near the above two hotels. You could try the much touted
Hostal Adriano (see reviews by doing a search) and also
Hostal T.I.J.C.A.L. . Simpler and cheaper hostels in the area would include
Hostal Oporto and
Hostal Aresol to name only a few. I've stayed at these last two and can recommend them.
I think we had a discussion (or casual mention) a year or two ago about how the prices at Hotel Carlos V had nearly doubled since the change from the Peseta to the Euro.
Anyone else with suggestions? Good luck!
Saludos, MadridMan