I have been many times, but unfortunately I think you will have a really hard time in finding something like Hostal Lopez in places like Rome and Florence. Spain is really great in terms of the relationship between price and quality for accomodation and food and Italy is notably more expensive.
You will probably not get away with less than 100 $ or so for a double room if you want a decent place in Rome, Florence or Venice.
There are a few monasteries in Rome that offer cheap accomodation, but they might have rules such as closing hours etc.
Good luck, anyhow, I would be pleased to hear that I was wrong and there still are nice little place that don't charge much
My experience is to the contrary.