I stayed in Roberta and Alessandro's lovely attic for 8 days in early July. I'd taken up their offer of a transfer from the airport for a bargain €35 and after arriving at the flat, Roberta welcomed me with a bowl of fruit and juice while she highlighted places of interest on a map of Palermo.
It really is a lovely attic and I felt quite at home there during my stay. The terrace was a great place to have breakfast and dinner, read and relax (I even soaked up the sun there after being advised to avoid Mondello at the weekend).
The flat isn't in a touristy part of town, which I felt was to it's advantage. There are local supermarkets and stalls and a bigger market 5-10 minutes away. The old town is a 15 minute walk away and it took me about 20 minutes to walk to the stop for the 806 to Mondello.
If you're looking for a chilled, affordable and comfortable place to stay in Palermo, I'd highly recommend this apartment.