We had a fantastic stay at Old Kitchen. Simone and Annette met us on arrival and gave us some fantastic tips and restaurant recommendations. We can definitely recommend nearby L'Archetto, and La Fraschetta in Trastevere.
The accommodation had everything that we needed for a base, and is situated in an amazing traditional Italian apartment block. Fresh croissants arrive at about 7.30 each morning for breakfast, courtesy of the bakery downstairs. The fridge is well stocked with cheeses, juices, milk, yoghurts and fruit. There is also bread and fresh coffee courtesy of the bean-to-cup coffee machine. There's also tea available for tea drinkers.
Old Kitchen is really well situated for getting to The Vatican City for early starts. It's about a 10-15 minute walk, and was perfect for us. The nearest Metro station, Ottaviano, is about 5 minutes round the corner. We got the bus from Ciampino airport to Termini station in Rome (45 minutes, 9 euros return ticket), then the Metro to the accommodation (1.5 euros). For the rest of our trip/sightseeing, we didn't use public transport at all, we just walked everywhere.
We would definitely recommend Old Kitchen and would happily stay there again.