Chianti Classico (with the black rooster label) is the real deal. Skip generic 'Chianti' bottles.
Chianti is 30 min south of Florence — easy half-day or day trip. Wine bars in Florence stock excellent regional wines.
Classic Florentine reds: Chianti Classico, Brunello di Montalcino (pricier), Vino Nobile di Montepulciano.