This is one of the (rare) occasions that I find myself disagreeing with Jessica.
It really depends where you're travelling in Italy, and what type of photos you intend to take. I was in Rome last year, and I found that with the narrow streets and small-ish squares, you really couldn't 'zoom with your feet' and back up to fit things on.
Both these pictures I've included here were taken with the equivalent of an 11mm lens on your camera. For the entire time I was there I mostly used the widest of my zooms.
If I were you, I would either go for a wider lens, or shoot what you have and add to it a 50mm f1.8. This will give you a much better lens for low light work - in restaurants in the evenings, indoors etc. It'll also give you a better ability to pick out details and let backgrounds go out of focus.
A longer lens may be useful - but only really if you're outside towns, or if you want to try and pick out faces in a crowd.
My main advice though would be for you to go onto flickr and search for pictures taken at the places in Italy you're travelling to. Flickr usually has camera and lens details for uploaded photos - and you can see on a picture by picture basis which lens was used for the photos you like. It's better for you to be buying lenses that reflect your own taste than my taste!