I really enjoyed my stay at Rita and Beatrice's lovely apartment. As a solo female traveling without a car, the apartment is conveniently close to a train station where you can reach the airport as well as the city-center in just under half an hour, and overall I felt quite safe in the tranquil neighborhood. Tram service is also an option, with a stop just across the apartment building. I will say though, and this is a problem that relates more to Palermo's public transportation system, that traveling between the city center and the apartment required quite a bit of planning and coordination. The train comes by every half-hour or so, so if time is of essence for you, keep that in mind. On most days, it felt easier to save myself the €1.70 per train ride (€5.90 to and from the airport, by the way) and just go for the 30-40 minute walk to the center.
The apartment was exceptionally clean and having full access to the kitchen was convenient and felt very welcoming. My room was clean, spacious and comfortable. Every night I slept like a baby, so no complaints about noise or the comfort of the bed. Although the apartment is on a 4th floor (or 5th floor for us Americans), there is an elevator that takes you right to its doorstop.
Communication with Rita was easy and clear, although I only had the pleasure of meeting in person with her daughter, Beatrice, who was exceptionally kind, accommodating, and helpful. As someone who is learning Italian, I always appreciate every opportunity I get to communicate in the language, although Beatrice speaks English and Spanish with no problem at all (I know this to be true because we spoke in all three!). I arrived rather late at 22:30, but Rita and Beatrice allowed me to check-in when I did without any problems. There was also another gentleman in the apartment, but I didn't have the pleasure of a formal introduction, although he was very nice and even gifted me a bottle of water since I couldn't drink from the tap.
Overall, I highly recommend you stay here. You won't regret it!