Given the city's superb location between the Chianti region directly to the north and the Vino di Nobile and Brunello areas straight to the south Siena is perhaps the best place to find just about every style of Tuscan wine produced.
The state-run Enoteca at the fortezza just off the Piazza Gramsci is of course the best place to start. Fortunately there are also a number of wine shops in the city that will offer you a taste of a wine or two. You can also find a few wine bars in the city as well.
Our personal favorite is still Aimone Piazzi's Cantina in Piazza.
Aimone's palate is impeccable (that's him on the phone above) and he deals only with the best producers -- in our opinion Aimone is all about discovery of great wine. These people are not just Senese, or Tuscan but etruschi, Etruscans. They know the meaning of the good life. And Aimone's right-hand is Alessandra -- from Livorno she knows both the vagaries of the sea and the nuances of Tuscan wine.
You can find them on Via Stalloreggi just across from the Hotel Duomo. Or you can visit them online at www.cantinainpiazza.it (in Italian only).
Two more wine shops worth a visit are the Enoteca San Domenico, which, as you might expect is just across the street from the church by the same name; they have a broad selection of local wines and products.
And Le Bollicine, just off the Piazza del Campo, at the corner of Via Rinaldini and Via Banchi di Sotto, has a very large selection of wines are very good prices.