Venice. Next question?

I would second Venice as we've enjoyed it every time we've been.

luci

Lake Garda area is especially chilled out.My favourite places are Bardolino and Garda Town.
Also like Lake Maggiore and Lake Como.
Less touristy places are Lake Orta and Lake Iseo.

Although I love Venice, have visited it often both as a tourist or as a Tour Escort I wouldn't say it was a destination for chilling out. It's more often than not crowded and hectic. Depends what time of year the OP wants to visit the country. In winter Venice can be foggy, wet and often the temperature is bone chilling.

The very south of Italy can be quite mild in winter but it can also be wet and cool.
In Autumn and Spring I would agree with holidaylover that the lakes would be the best. Italy over the winter months is more of a destination for short city breaks or ski-ing which is usually anything other than chilled out.