missmadrid98 is correct. I think the biggest complaint I hear about Madrid is that it can be difficult to get a good night's sleep, particularly in hostels/hostales because they are often poorly insulated and rooms often face busy streets or are near bars. But then, this describes about 99% of Madrid now doesn't it.
I think only the bigger hotels (the higher, the better) will give you a quiet night...unless you're facing the Gran Vía.
Anything around the Plaza Mayor will be no exception. It will be busy in this area. There's only one hostel/hostal next to the Plaza Mayor which has a website, Hostal Macarena
, and you can't reserve via email - only by phone/fax.
Plaza Santa Cruz....? Hmmm... Do you mean Plaza Santa Ana maybe? I'm not familiar with Plaza Santa Cruz. If you mean Plaza Santa Ana (not far from Plaza Mayor) then this place is HOPPING until dawn. In fact, I received an email from one person recently who had a hotel on the Plaza Santa Ana and they complained of traffic, bar noise, and shouting pedestrians in the early early morning hours.
Some hostels/hostales in the area around Plaza Santa Ana would include Hostal Lopez, Dulcinea, Martin/Cervelo, and a few others. You can find their links and others on MadridMan's Madrid Hostels
Have a great time in Madrid and be sure to come back here and tell us all about it, including where you decided to stay. Afterall, YOUR experiences help ALL of us.
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