The apartment is extremely well located. Basically, you become the Pope's neighbour.
If you stay, take note of the number of the house closest to the nearby main street (Viale Vaticano) and use it if you need a taxi, it will make your life much easier.
That being said, "Cosy" means "small" in AirBnB. If you are over 6ft2, you will not stand upright in the living room. At 6ft tall, I couldn't take a shower standing, and had to bend to get in the kitchen.
The building's elevator was malfunctioning for our entire stay. Not Alessandra's fault, of course, but you may want to make sure it is working (there was a sign on one of the floors, so it may be a recurring issue) , because dragging two loaded suitcases up to the 4th floor and back down was not fun.