Chiara's place is a great base for visiting all that Rome has to offer!
The apartment is well served by buses and a short walk (10mins ish) from a metro A station. It's also right next to a metro C station but that line isn't particularly useful for getting into central Rome.
However, the flat is also very walkable into central Rome and we tended to walk everywhere except the Vatican (which is easy to get to on the metro). The colosseum is about a 30 min walk and everything is very accessible when you are in central rome. I would strongly recommend walking around as it means you stumble across lots of unexpected treasures!
But, as I said above, it's easy to get home using public transport if you're tired after all the walking.
In terms of food, there's an area called pigneto very near to the apartment with several restaurants. I would also recommend heading over the river to trastevere (via bus or from central) as this area has a number of bars and restaurants. By taxi it was around €15.
Getting to the apartment from the airport I would recommend getting the train to Tuscolana rather than Termini as it is closer and cheaper!
Finally, Chiara was a lovely host. Very communicative before the stay and there to greet us and talk us through the apartment.