I would highly recommend Luigi's place for a stay in Rome.
Highlights:
+ Location, location, location - it is literally waking distance to all major attractions, with a kid we could reach Colosseum in 15-20 mins, Spanish Steps / Trevi Fountain and Piazza Novona in less than 1/2 hr. The only time we took public transport was when we went to the Vatican. Even Roma Termini is quite close.
+ There are supermarkets and eating outlets nearby.
+ The apartment is cozy and comfortable, it has all the basic utilities that you need (Does not have a microwave, has a very small oven though).
+ It is ok with kids. We had a 3 yr old with us.
Lowlights:
- The bed makes a lot of noise. When you turn in your sleep, you end up waking your partner. I requested Luigi to check on this as it was a big irritation for us. Hope he fixes it soon.
- The kitchen is very small. It is literally 2 feet in width, hardly any space for anything, if you plan to cook and eat, this is not an apartment for you. Only basic heating and tea/coffee would be ok.