We have just spent about 5 days looking for a place and found one in Palermo, ad I have to agree with PostMod for the most part.
First, a lot of temps especially on Craigslist, and through agencies are "expensive" compared to the overall inventory. They are totally geared to tourists. Sure if its vacation they are good deals compared to a hotel, and as nice as any Hotel if not better, but they are not long term.
The problem however, (and we had this) is that unfurnished apartments (as most locals rent) are much much better deals, but they generally require a 2 year committment, a guarantor (who is someone that must own property in the Cap Fed city district), and completely unfurnished (a stove thats it,..not even light fixtures). So you will have to buy a fridge, a bed, furniture, plates, etc... so unless you know "I will be here for two years or more" it may not be worth it, even with inexpensive furniture.
That being said, we saw 2 amazing "local" apartments for under U$S1000 (all expenses including internet, cble, but no furniture.) But amazing about 950 sq. ft, french style, doorman, terrace, top floor). But they were on busy avenues and maybe not the ideal neighborhoods. I am sure more are out there, but in the end we decided to find a short term place until we get more of a feel for where we want to be and how long. $700 1 bedroom, with a den (for baby), with outdoor space, all expenses (internet/cable), in Palermo.
We used a friend of a local friend as a broker...and he was amazing. PM me for his name and he can help for sure. I can also share our experiences.