Rome: Der Pallaro, Pizzeria Pannettone, Osteria d'augusto
The pizzeria is the one better known by its nickname, L'obitorio, the morgue, for its marble tables. It's good, also loud, always crowded, and -- at least used to be -- better suited to, say, grabbing a bite before a movie than spending a leisurely evening. It's on Viale Trastevere and is an institution. I used to go there before the movies at the Pasquino because it was fast, but they closed the Pasquino and I haven't been to the obitorio since.
Pallaro is near Campo de’ Fiori and has its staunch fans, but it is better loved, by those who love it, for its price-quantity ratio than its price-quality ratio.
Augusto, in Trastevere, is an old-style paper-tablecloth joint serving a very traditional menu. Here too, the main attraction is that it's cheap. Some people see charm, others not so much.
What all three have in common is a low price and relatively central location. Although there must be people who love the food for itself, possibly neighbors who have cultivated relationships and favorite dishes, usually the main attraction is the price. L'obitorio is a possible exception, because the pizza is (or used to be) quite good.
Pannettone actually is named Panattoni or l'obitorio as Maureen guessed.
I still go there when I want a quick Roman thin pizza, especially when it's very late and it's not easy to find other open places serving food at the table.
Der Pallaro has a fixed menu and it is not between my favourites restaurants. It's some years I don't go there but reading the comments it looks like it is not changed so much with time, except for price that currently should be 25 euros per person.
Largo del Pallaro 15, Rome, Lazio 00186, IT
I love the number of nicknames some of the Roman places have (like ai Marmi)
it can make it hard for visitors like me to sort it all out sometimes
Piazza de' Renzi, 15,, Lazio 00153, IT
Pizzeria Ai Marmi AKA L'Obitorio AKA Panattoni
Viale di Trastevere 53-55, Rome , IT