jacmom, do you mean "hostales"? If so, then yes, but they're called "Pensiones" - spelled the same as in Spanish. I've stayed at a couple of these in Rome and also in Florence, Italy. I don't remember their names (it was in the early 90s) but they were family owned and operated budget hotels just like in Spain (at that time - surely they're much nicer now just like the "hostales" are much nicer now too).
Try a search using, for example, the following search syntax:
pension +roma
That should yield quite a few. Good luck!
Saludos, MadridMan
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