Hi squeakr,
Since no one has replied, I'll give you some of my opinions about places to stay.
First, if you're looking for air conditioning, all of the hostels I've ever stayed at in Madrid had air conditioning. The air doesn't get as cool as the air in the U.S., but the rooms are comfortable.
If you're looking for a real quiet place, then staying near the center of Madrid, i.e. Puerto del Sol, is not for you. However, even around the center, the noise isn't too bad, especially if you are at least four floors up. Also, generally, though not always, the street noise dies down at around 11 p.m. But there is the occasional noise from other people living in the same building as your hostel. For this, stay away from Hostal Dulcinea.
And finally, as for safety. The crimes I'm familiar with in Madrid are non-violent. I'm talking about pickpocketing and other schemes to get your money. In my opinion, these are a constant threat in Madrid. If you are always mindful of your valuables and about where you are in Madrid, you will minimize, not eliminate, the risk of falling victim to these types of crimes.
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"I swear -by my life and my love of it -that I will never live for the sake of another man, nor ask another man to live for mine."