Two weeks in Italy

What time of year are you planning to come?

San Gimignano is heavily touristed. Choose another town in Chianti to stay( Panzano, Rada, Castellina, Siena) and take a day trip to San Gimignsno.
If you like less touristed places skip Tuscany and visit the Piemonte which works well with the Cinque Terre ( also very touristed, consider Santa Margherita Ligure or Porto Venere) and Lake Como. The Piedmonte has charming wine villages. We were based in Alba and found it very convenient.

Given you are flying something like 10k miles, I suspect the day you land and the next day are going to be a jet lag fog, if all you have is two weeks you are going to want to minimize the number of times you move. Find no more than 3 strategically placed locations from which to do day trips.
Where you arrive/depart Italy will be important to your choice of locations.

Consider staying for at least 3 nights in Bologna. It's a pleasant town with great food but the best reason to stay there is that it's a rail hub so you can easily day trip to other towns to sightsee during the day, then either stay for dinner or return to Bologna to dine. You can visit Modena, Ferrara, Padua, Ravenna and others.

If you can, it's best to fly into Venice where you can get over the jetlag while soaking up the atmosphere. If not Venice, Milan would be my second choice. You can go to Como or Venice (or Verona) by train if you arrive fairly early in the day. If you aren't going farther south than Tuscany, it could be better to fly out of Milan than Rome. I haven't been to Como, but it might be almost as good as Venice for the start of your trip - much less stressful than rome or Florence.