The apartment is close to the Roma Termini train station, about 5 blocks, and you can walk to the Colosseum, the Roman Forum and Palatine Hill in about 20-25 minutes. all the other sites from there were about 15 -30 minutes.
Since we would get up early, we walked to the Termini station to get breakfast and coffee since the surrounding shops would not open early. They also close early. Most of the restaurants we ate lunch or dinner were near the sites we visited.