Hi Ron,
When are you coming to Rome? A lot depends on what's in season. It's bad for local agriculture, for the environment, and for your tastebuds to eat out-of-season foods -- so if you're not coming between February and May, for example, try not to binge on the carciofi (artichokes), which won't be Italian, but actually French.
Some year-round favorites of mine:
-the trifecta of Roman pastas: cacio e pepe, carbonara, and amatriciana. I especially like Roma Sparita's cacio e pepe, presented in a basket of parmesan. The restaurant's on a lovely piazza in Trastevere and has lots of other options for pickier eaters, including pizza.
-thin-crust Roman pizza. Pizzerias like Baffetto or La Montecarlo are right in the center, but I find that while their pizzas are good, the service is incredibly gruff, even by Roman standards. Instead, I'd recommend either Da Remo or Nuovo Mondo, both in Testaccio, or Formula Uno in San Lorenzo, just outside the city center and very easily accessible by bus or taxi).
-Rome's fried offerings, including fiori di zucca (fried zucchini flowers with cheese - in season July through November), olive ascolane (a fried olive mix), and filetta di baccala (fried salt cod). One place that does fried foods really well is Al Pompiere, in the Jewish Ghetto.
-offal. You might even be able to sneak some by the pickier eaters, especially pasta with coda alla vaccinara (oxtail), if you don't say anything! Other things to try include trippa (tripe) and pajata (the intestines of a milk-fed calf). One of my favorite places to try this is called Il Pommidoro, in San Lorenzo.