Some good suggestions so far and there are so many places to suggest it kind of makes it hard as Italy is quite big and not everything is so close together.
What kind of things would you like to see?
Do you prefer to base yourself in a city, by the sea, mountains or by a lake?
What time of year?
Would you like to stay in one area or will you hire a car to travel around?
As as you say you have never been before, I presume you will arrive by air? The main International Hub airports are
Milan (In the north) and
Rome (Central Italy) although some of the smaller international airports do have flights worldwide and many have direct flights with other European cities.
Without knowing the above it's very hard to suggest, however if you was to arrive in
Milan during the summer months, I would suggest you visit the
Lake Garda area. The lake is very big and has something for everyone. (except for the sea) Also, you could do some day trips to
Milan,
Verona or
Venice as they are a short train ride away. (within a few hours)