Rome restuarant suggestions? trastavere also?

Trastevere has some very tourist-oriented places so beware. Two I can recommend are Dar Poeta and La Gatta Mangiona, both pizzerias. I have heard good things about Trattoria da Cesare but I have not been myself.

Near Piazza Navona, try Antica Taverna. Lots of Romans eat there. Good Roman food and reasonable prices.

Not the right neighborhoods, but I had the best cacio e pepe of my life at Flavio Al Velavevodetto in Testaccio, and of course Bonci Pizzarium is deserving of all the praise (and only a 15 min walk from the Vatican if you are over there anyway)

Another vote for Dar Poeta. We always go there for dinner on our first night in Rome. Great pizza and salads. You can eat outside or indoors. It's on a small side street in Trastevere. Another more formal but not fussy place is Le Mani in Pasta, also in Trastevere. We have had dinner there twice on two different trips and each meal was memorable. We plan to go back to both places in June. Good home cooking in a friendly atmosphere. They give you a small glass of prosecco on arrival. Last time we were there, we had a table in front of the kitchen and got to watch their fabulous chef in action. Everything is made fresh for each order. He actually cuts up the onion, the zucchini, boils the pasta, etc right then and there. Nothing is prepared ahead of time. Everything is delicious. If you don't mind eating dinner very early, you might be able to get a table without a reservation but otherwise, making a reservation might be a good idea. After dinner, you can take a stroll to nearby Fior di Luna, one of the best gelaterias in Rome for gelato.

When in Rome, we do usually stay in the Trastevere. Some of our favorites are La Scala for a bit more upscale option. Yes, Dar Poeta for pizza (though worried that they are getting so popular), and Popi Popi, a good casual place with good pizza and quite a few Roman dishes. We have also had luck just wandering the back streets, finding a little family spot and looking at the menu. I honestly can not tell you any of these places, we found them, had a great meal, not sure if I could find them the next day or remember a name or address.

Hostaria Da Settimio
Via Val Tellina
(Monteverde)
No written menu
No English spoken
No tourists of any nationality
Just Romani de Roma (Romans of Rome)