Coming from the UK I know how it feels when you go on holiday and as soon as it gets a little bit hot you need to put your flip flops on and a skimpy little vest top. Well they don't do that in Palermo, I know what you're thinking - that's because they're used to the heat - but really it's more of a dress code, flip flops are for the beach and vest tops shouldn't be so skimpy that you lose any dignity. But if you don't mind looking like an obvious tourist then wear what you like, apart from inside churches where you must cover up.
I found it very very mediterenean and remember the 'siestas' when everything was closed and there was absolutely nobody on the streets. This is unlike in the bigger cities in the North of Italy. (Palermo is Italy's 4th city after Rome, Milan and Naples). I have travelled in the south of Europe but only found the 'real siestas in smaller villages (real siesta when a place is really 'dead'). I found the siestas very typical and a bit strange in a big city like Palermo and of course for a girl from the netherlands. But it also gave the city and region character.