From April 28 through 30, 2014, a friend and I stayed in Palermo at Bed And Breakfast La Bella Vita: http://www.bblabellavita.it/?lang=en. This is a small place (only four rooms). What a find! Each room is large and has a balcony, the bathrooms are large (with a really nice stall shower), the owners really want to make sure you have a good stay, and it's really cheap (only €55 per room for night for a double for single use; rates vary slightly by season). The neighborhood is perfect; it's between the old city (a bit gritty to stay in) and the fanciest area (a bit too fancy for my taste, with lots of famous designer's stores - Gucci, Prada, etc). There are lots of nearby restaurants, and it's only about a 10 minute walk to the port. It's near the buses to the old section (on via Ruggiero Settimo, a block from the hotel) and from the old section (on via Roma, a block in the other direction) if you don't feel like walking.
The hotel itself is on a traffic-free street, so it's quiet and sitting on the balcony is very pleasant, even though you're in the middle of the city. We paid an extra €35 to be picked up at the airport, and it would have only been €45 for round trip airport service (in both cases, cheaper than a cab). This had the added benefit of delightful conversation with the owners on the way in. The WiFi worked well.
The only (potential) negative for some is that in one-quarter of the toilets in Sicily, you cannot flush toilet paper, but must deposit it in a small basket (like in Turkey or Brazil or Russia, among other places). I never did figure out the rhyme or reason to predicting which toilets this would affect (it wasn't consistent in a city or neighborhood, for instance). At this B&B, you cannot flush toilet paper (the only one of our four Sicily accommodations where this was the case).
I would DEFINITELY stay here again.