You might look at
www.hostelbookers.com. My son and I stayed at Village Roma last December. Really inexpensive, but workable. The rooms are halves of little trailer houses. Shower, refrigerator, on a bus line, and across the busy street (a walkway over) is a huge supermarket. Never ran out of hot water.
You have to either rent or supply your own towels, but bed linens are included. The only problem we encountered was the unit wasn't tied down like a fixed trailer house is suppose to be. So - any walking, tossing in bed, etc. from either your side or your neighbors shakes the whole unit.
Oh yes, and the heating system is kicks in very noisily. Ear plugs solve that. Otherwise the area is very quiet.
There are other places on the site, its just that this is the only one I have experienced.
Spotlessly clean.
And the One Euro wine from the supermarket is very good.
Note the 40% discount for stays 3 nights or more. Makes it really reasonable.
Romelle