I was waiting for someone else to make a personal recommendation and usually, by now, someone on this board would have offered a couple. Since it's been almost four years since my last visit to Madrid, I consider my self ill-suited to the task, but here's my advice/opinion.
I'm not really for sure what you're requesting by a "nice, not too young" Hostel. Are you looking for a quiet place to stay? If that is it, you probably want to stay away from central Madrid, that is, around Puerta del Sol. I've stayed in two Hostels around the center and they were moderately noisy. Fortunately, even these weren't noisy every night, just the nights that I had to catch an early train.
As for the nice part, both Hostels I stayed in, Hostal Dulcinea
, and Hostal Madrid
, were very nice. Far from luxurious, they were clean, had single beds and a nice, if not large bathroom.
I hope this was helpful, and the MadridMan is right, there are hundreds of reviews on this board if you want to review them.