In terms of prices in Rome, what are you looking at? Just back from Copenhagen which was very expensive (although could have done it on a budget if really wanted to). Is public transport the best way to get around?
Think Rome -> Palermo is doable, seems to be reasonably-priced flights operating that route in the summer.
Not sure what Copenhagen costs as a comparison point. We had saved up for a while for the trip, so didn't go too discount, though we tried to eat cheaper (pizza pizza pizza) most days and splurged once per city we visited. We did use the metro to get around and our hotel was located near the Termini station, where the two lines cross.