You will need to have a dinner reservation as everyone seems to dine out and the restaurants book early. You might want to try to get something set up now. Be aware that Italians that normally dine late dine even later on NYE. They start about 10PM. The restaurants we have been to (lived there for several years) always have party hats and noisemakers for midnight.
Fireworks start everywhere at midnight: big displays in sanctioned places, private shows off of tiny balconies, and general misbehavior in the streets and piazzas, so be careful. People get carried away -- at least pre-COVID they did - in Piazza del Popolo. You'll want to Google "Rome New Years 2021" to see what official events, if any, are planned. If not, there will be plenty of unofficial revelry.
Plan to walk as by midnight the streets are jammed and the buses stop running in the center. Taxis are rare and as mentioned above the Metro is nuts. I often thought it would be fun to get a hotel room overlooking the Colosseum t watch the show there rather than be in the street, but we just ate in our neighborhood and watched the fireworks from balconies near us. The displays went on for over an hour all over town.
Get some red underwear. It's a thing.