Itsly

It depends on your interests, but you can't visit Italy from one base only. The country is too large. You may want to consider to go to various locations, for example for a week or so in each place. One place is certainly Florence and Tuscany, Rome is another, but the choices are many.

Do some research on your own based on your interests, then come back when you have more specific questions. It’s your trip, go where you want.

Agree with the above. Also, which month do you have in mind? The South gets very warm in July-August, with the odd June heatwave too - this includes Rome and is worse in Naples and points south.
Conversely, the North (including Bologna and points west and north) is not at its best in late fall and winter.

Not only will you need multiple bases, you cannot see all the great places in Italy in a month. That's why we need to know what sort of thing you're most interested in--so we can tilt our suggestions in that direction. Knowing your interests and the time of year are key to helping you. Are you interested in:

Classical ruins (Roman? Greek? Etruscan?)
Ancient artifacts
Gorgeous churches (any particular style--Romanesque, Gothic, baroque?)
Art museums (which periods?)
Palaces
Castles
Historic buildings
Street markets / life on the street
Vineyards
Food-production facilities (cheese, balsamic vinegar, prosciutto, etc.)
Scenery (mountains? coastline?)
Hiking
Water activities

Keep in mind Italy is a lot like CA. How would you answer that question for CA?

Thank you all..,you all blew me away with your suggestions
Some more information:
I want to go to market places. Go shopping.

Just relax and see little towns, get the real favor of Italy. Take a cooking class.
I want to be centralized, near transportation.

Thank everyone again.

Buy Rick's Italy guidebook (or read it on the website). Look at his various suggested itineraries, come back with questions.

Or at least watch some Rick episodes for ideas.

Just relax and see little towns, get the real flavor of Italy. Take a cooking class.
I want to be centralized, near transportation.
Where should my home base be?

Italy covers an area roughly equivalent the area of Florida, Georgia and S Carolina.

Where would you base yourself to do there what you want to do in Italy?

Folks here are happy to help, but it's hard to know if the string is long enough if we do not know how high up is.

You might just want to do a region- say Sicily or Tuscany and not try to see the whole country. If so, you absolutely could home base and then explore from there with a focus on markets, food, cooking etc.

Dave,

With a month to spend and I'll assume this would be your first time in Italy, I would think Rome would be a good place to start. A week in Rome and then head either north or south (or both). As RS says if you like Rome, try out the Naples area, it's even more intense, but you also have Pompeii, Sorrento and the Amalfi coast to enjoy (this includes Capri). If you are interested in a more rural scene, Tuscany and Umbria would be a must (actually, in MHO, they are a must see). From there, head up to Venice and perhaps the Lake Como region.

I've never been disappointed anywhere in Italy.

From what you hope to do, Tome then a town in Tuscany should meet your requirements well.
In Tuscany look at Siena and the villages in Chianti.