Recommendations for restaurants in Travestere area or near the City Center in Rome?

I have three places I usually would hit on a trip, all different.

Now it is a Rick Steves pick, but early on it was just a great pizza place, Dar poeta serves great wood fired pizzas in a cramped but funky space. Make sure you get the dessert Nutella/Ricotta calzone. http://darpoeta.com/

A bit upscale would be La Scala in Trastevere. Nice selection of Roman and Italian dishes, nice if the kids can tolerate upscale, but more trattoria than fine dining. http://www.ristorantelascala.it/

A bit more Family Italian would be Popi Popi, it is more working class, great Roman dishes plus pizza, big space, casual, kids are no problem. (no direct website, but Zomato has a menu) https://www.zomato.com/roma/popi-popi-trattoria-trastevere/menu

Dar Poeta is a hoot and I heartily endorse Paul's recommendation. Another great pizzeria is La Pratolina in Prati, and Da Remo in Testaccio is a good mostly local experience.

We always loved Antica Taverna which is just west of Piazza Navona. Not sure how it has held up since we left Rome in 2016, but the ownership is the same, so probably still good. Very reasonable prices!

These were my favorite places of the many we tried a few years ago.

Trattoria Da Enzo! - In Trastevere

Enoteca Cavour 313 - Near the Colosseum

Il Sorpasso - Near the Vatican

I liked Da Enzo, too. It's an extremely down-homey sort of spot (if it were in the US, you'd walk right on past it), but known for Roman cuisine and reportedly popular with off-duty chefs. Make a reservation.

I've not had a bad pizza at Dar Poeta. Finding it is fun, eating there is good, people are friendly but not all over you.

Restaurants that we enjoyed In the Travestere area were Marco G's and La Crucia (a RS recommendation).

Enjoyed a Sunday Night dinner at Trattoria Da Lucia. Small place, not fancy, just really good food after a day of wandering the lanes of Trastevere. Would recommend for families.