A fantastic location and very kid-friendly. We walked just about everywhere from this apartment--Vatican City, the Coliseum, the Roman forum--and only had to get buses to go to the catacombs on the outskirts of the city and to the train station. One tip we appreciated was good local restaurants to try; the one we went to in Trastevere, Meridionale, ended up being our favorite in Rome.
The owners were very accommodating, meeting us on arrival even though our flight came in late and allowing us to leave our bags in the apartment after we checked out for a few hours. They have also made this a great place to come with a child. The apartment is equipped with a crib and high chair, toys and books.
If you like to make your own coffee in the morning, do bring a French press and ground coffee.