We stayed at Domenico's apartment for 6 nights with our 9-month old baby. Upon arrival Domenico met us downstairs and showed everything to us. He also left some complimentary breakfast and a bottle of wine, so very nice! There were a baby chair and a comfortable baby cot for our boy. Everything was very clean.
It was very hot in Rome so air conditioning was a big help! At night you could open the windows and only hear the neighbours and not the noisy nearby streets. The hot water supply is enough for three to take a shower. And having a washing machine and even a dishwasher is a nice bonus.
The metro is one block away, though we didn't use it as the Prati area is well reachable on foot, as well as the historic centre. There are also buses and trams to get around. A couple of supermarkets, very nice bakery (even two), a famous coffee shop all a few blocks away, several bars within one block (the cheapest one is on the other side and across the street) and even offices of mobile operators if you need a local sim card (btw there is descent wifi in the apartment so it might be enough for you).
Domenico recommended us a very nice family restaurant and we had a wonderful dinner there. There are also a few more very good ones in the same area and a couple of irresistible gelato shops.
The only concern we had (very common for all Italy though) is the elevator - it was too small to fit our stroller and had a couple of stairs to reach it, so we used to fold the stroller and just hold our son. But having even a small elevator is definitely better than having none!
We had a really lovely and relaxing stay in Rome. Would definitely come back and recommend Casa Dom to our friends!