Walking peacefully in Rome-which are the very trafficked streets?

People could be more helpful if you said where your hotel or apartment is located.

We stayed in Trastevere and found quiet ways to walk almost everywhere, to the Vatican, the Colosseum area, and even to Villa Borghese. But the routes might be different from your location.

You can probably do this on your own, but anything that looks bigger on the map is probably bigger, so Via del Plebiscito/Corso Vittorio Emanuele, Via del Corso, Via dei Fora Imperiali, Via di Porta Cavalggeri are all busy streets....as the historic center has smaller streets, anywhere on your map that you see a bus stop I would assume is larger than a pleasant side street.....

Have you tried using google street view to see what the streets actually look like? One of the nicest walks I had was down the Appian Way. I took a bus to a location close to it and then walked for quite a while, going into s few sites along the way. Didn’t see a single car once I got to the original ancient cobbled road.

West of Piazza Navona and near the river, Via Giulia and Via dei Banchi Vecchi are nice, quiet streets. You might check out Via del Governo Vecchio, too--though I didn't have time to walk down that one.

Farther north, basically NNW of the base of the Spanish Steps, is the Via Margutta, a lovely change from the hectic Via del Corso.

The Monti neighborhood is great for wandering, too.

The suggestion to zoom in on Google Maps and avoid streets with bus-stop icons is an excellent one.

Thanks for all these great ideas!
We are staying in an apartment a block or so from Piazza Barberini and would like to walk everywhere from there, except we are not going to the Coliseum this trip.
Does the area of Plaza Barberini have lots of car traffic? Just wondering.