SF to Tuscany

Check flights on www.kayak.com. If you want a round trip to/from the same airport enter
from: SFO
To: FLR
for the destination click on the "nearby airports" option box. That will give you results for both PSA and BLQ as well.
Pisa (PSA) is in Tuscany, Bologna (BLQ) is not, but close (60 miles north Florence). If prices are cheaper, you may not mind the extra hour drive (and the extra gasoline+tolls).

The best way is to fly non stop from SFO to a European hub, then from there proceed to either FLR or PSA (or even BLQ). I avoid to connect via the East US airports (JFK, EWR, IAD, or ORD) like the plague. I'm willing to pay more to fly directly from SFO to Europe. Stopping back East first will greatly prolong your journey (and aggravation).

I go to Florence often (once or twice a year) and my preferred option is with Lufthansa. Since SFO is a United hub and Lufthansa and UA are both partners in the Star Alliance, that option offers the most flights, especially via Frankfurt (FRA) but also via Munich (MUC).
So I usually fly:
SFO > FRA (or MUC) > FLR
There are 3 dailies to FRA (one operated by Lufthansa and 2 by United) and one to MUC (operated by Lufthansa). The flights are codeshare with United therefore they have both LH and UA flight numbers.
Although FRA has more flights, however I prefer MUC airport. Much easier and faster to connect. FRA is huge and sometimes I have to run to make my connection to FLR.

Other good options from SFO to FLR with one stop only are:

AirFrance via Paris - Charles De Gaulle (SFO > CDG > FLR)
KLM via Amsterdam (SFO > AMS > FLR)
Swiss (part of Lufthansa) via Zurich (SFO > ZRH > FLR)

I've tried them all and they all work. However CDG is a huge monster airport and not quick to transfer flights. So if you go that route allow at least 2 hours layover to FLR. But at least AirFrance has the most flights to FLR (6 or 7 dailies), so eventually you'll get there.

London LHR is not a good option. There are numerous non stops from SFO to LHR (British, United, Virgin), but there are no flights from LHR to FLR. However British has 3 dailies to BLQ.

PSA is mostly a Ryanair and other low cost European airlines airport. It is possible to be reached from the US however with AirFrance (via CDG) or Lufthansa (via MUC only, as PSA is not connected to FRA).

PSA also has a non stop from JFK operated by Delta. It is 4 times a week but it's a seasonal flight that operates only June through August, therefore not good for you as you travel in May. Pisa is in Tuscany, 50 miles west of Florence, near the Tuscan coast.

FLR airport has a very short runway and wide body jets coming from North America cannot land there, Pisa is the closest airport with a runway long enough for transatlantic flights. However except for that Delta flight I mentioned, no one else is flying directly from the US.

Thanks, Roberto. Very thorough!