Now I recommend you one of the best pizzerias in Rome, La Montecarlo, with an acceptable waiting time, an affordable price, a casual atmosphere and of course many locals. It is located near Piazza Navona and you can easily stop by between a busy sightseeing.
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In Trastevere tucked away from the main tourist area in Rome, there are less restaurants, bars. The place like this is definitely you should go to find local restaurants. Trastevere has many of them and the one I am recommending is Le Mani in Pasta.
Which one is the best Gelato? As one of the answer to the esoteric question, I name Old Bridge, which is located near Vatican.
I'm recommending Hostaria Romana to people who are seeking a local atmosphere. They serve traditional Italian cuisine at affordable prices.