I highly recommend the apartments of Lucrezia (we tested 2 of the 3 that are located on the same floor). We were very well received with very useful recommendations for our stay (including a map of the closest transports, shops and good restaurants). The apartments are very well decorated with "designer" furnishings and very comfortable, very very clean.
The apartments are located in a residential area (near Notarbartolo station) at approx 10 min by bus of the Massimo Theater of Palermo: very easy to access, calm and clean.