It may be surprising to many, but sometimes there is preferred pricing in Europe. Having lived in Madrid, Rome, Copenhagen, and now Vienna.... when we were given a separate menu (English-speaking), there were, on occasion, separate prices and/or menu items. It does happen and yes, it was most prevalent (of the cities we've lived) in Rome. Like Laurel, dining in Rome we often asked for the Italian menu rather than the translated English-speaking menu. After a while, the Italians menus were easier to read and understand.
At the same time, - and I am sure Roberto would acknowledge this - there are separate menu items available to a local that are not even on the menu. Many times I would be dining with Italian friends and they would not even open the menu. They just told the waiter what they wanted.
But shouldn't being a regular customer have some benefits? In Rome, each morning on my way to work I would stop at the bar across the street from my apartment, order my espresso, pay my 80 cents (price listed on the wall) and be on my way. After about 2 months of this, the owner who I got to know in my very bad Italian and his limited English, said to me, "Sessanta." (60 cents). And from that day forward, "my" price was 60 cents. (My wife, who only went over perhaps once a week was still 80 - drove her nuts!).
We ate at least once a week at a restaurant on our street in Rome. The English/Italian menus were combined so the same prices were presented to all diners. Every now and then I'd ask for cacio e pepe which was not on their menu. I was never disappointed. After we became "regulars" we also got a lower price - usually about 10% off, or free desserts, free antipasti, etc. Granted we almost always gave it back in the form of a good tip, but there was acknowledgment of our status as regulars.
So it may not be as obvious as a separate menu, but "locals" or more specifically, regular customers, do get some breaks - and why not? They have to tolerate the influx of tourists as exemplified by Roberto's comments... Trust me, even though I am not Danish, Italian, or Austrian, I still got frustrated by the poor behavior of non-locals in "my" restaurants. Imagine going into the restaurant closest to your home and it being descended upon by people who do not know or - worse - do not respect your culture and values.
We saw it every day ...and still do here in Vienna. (Granted here, there are far fewer Americans acting the part of the boorish guest.... but it does happen). Perhaps 25+ years in the service industry has also made me more -sensitive to the challenges of the local restauranteur.
Certainly there are restaurants in Italy that DO gouge the non-local crowd. And the internet is filled with stories of these places. Perhaps the most famous incident in Rome was at The Passetto, near Piazza Navona. As a result of negative feedback, an international incident, and the ensuing inspection that reflected "health code violations," they were closed for a period of time - for remodeling... So best to report and avoid those establishments that do price gouge an unsuspecting tourist. Certainly that's a benefit of open forums such as this.