It all depends where you want to go for your holiday.
In the north west, you can do Venice, Padova, Verona, Mantova and Vicenza all very easily. They are especially good if you like renaissance history and architecture. You could also go to Bassano del Grappa as well which is a gorgeous town famous for its alcoholic beverage. I lived in the Veneto a couple of years ago and could never tire of it, although Venice can be a struggle at times as I hate over-touristy areas and times of year. Additionally the Venetians themselves aren't the most welcoming of Italians, but then many of them consider themselves not to be plain Italian.
Although it is nice to say you have stayed in Venice it can be notoriously expensive even out of season, and you can find far nicer places on the mainland 20 mins by train from Santa Lucia. Padova is a good hotel point as you can sleep there, "commute" into Venice, and spend one day in Padova to break up the trip.
Tuscany is obviously a popular tourist destination, but then why not? Florence is very attractive with the history and the centre doesn't make it feel like you are in a big town. Ponte Vecchio is a no-brainer, but there are also lots of palazzi and churches to go around, most having been associated with the Medici at some point. If you get a chance to go up the Campanile (Bell tower) or Brunelleschi's dome, then do it. Agree with Alec that you must go to Lucca if in Tuscany. I thought Siena is worth it too, but quite expensive. Best time to go is for the Paglio in July or August for the excitement despite the enormous crowds. Then there is Pisa... The problem with Tuscany is that it is so big, it is difficult to see lots of different places without travelling for ages. I only stayed in a cheap hostel in Florence, and I can't really remember any of the good accommodation areas. Eating wise, there is tons around Piazza della Signoria - cheap and not so cheap.
I haven't really done the south that much, but if you want Naples, don't forget Herculaneum and the Villa Poppaea for some more "preserved" stuff. The Campi Flegrei are pretty cool too.
There is a bit of history to Rimini, but I don't know why people want to go there - it is a bit like a cross between Ibiza and Blackpool! It has lots of clubs as well as a massive red light district... Urbino is close-ish, and Bologna could be a day trip.
Unfortunately, wherever you go which is touristy, the Italians have learnt to exploit with high prices and hassling tactics to get you into restaurants (especially Venice). Careful of pickpockets, and try not to buy anything from the immigrant street sellers because if the police catch you doing it, they love to turn the screw and fine you for buying counterfeit instead of the vendor!