Puglia-flights to southern Italy

From LAX I presume? I'm sure there are other options but LA>Rome>Bari on Alitalia is an easy and as direct as you'll get option. I did it in reverse, had no problems.

You are pretty much left to the mercy of Alitalia. All other choices are low cost intra-european. You can fly to either Bari (BRI) or Brindisi (BDS). Therefore the fastest flight would be: LAX>FCO with Alitalia (Delta codeshare)
FCO>BRI or BDS

Thank you. That is what I am finding out. I am taking cooking classes in Lecce and also staying in Monopoli. Any favorites from this region? We are also interested in pottery towns.

Alberobello and its trulli are a must if you go to Puglia. It's not too far from Lecce, but closer to Bari. Castel del Monte is another major one, but it's a little far from Lecce, close to Foggia in the north side. Closer to Lecce and the Salento area, you should go to Otranto, Santa Maria di Leuca, Gallipoli, Castellana's Grottoes. Lecce has some major Roman amphitheaters. It's been a long time since I went last to Puglia (in the 1980's) but I remember vividly the beauty of the sea and the coast. And of course the food. When you go to the cooking school ask them to teach you these dishes: Orecchiette con le cime di rapa (orecchiette with broccolini rabe) Orecchiette alla carne di cavallo (with horse meat) Risotto ai frutti di mare (seafood) Polipo alla griglia (grilled octopus) Cavatelli con le cozze (cavatelli with mussels) or anything with mussels. Melanzanata di Lecce (eggplants) Linguine ai ricci (with sea urchins) and of course get a puddica when you are there (it's a sort of a pizza).
The specialty in the coastal areas is obviously seafood and fish. One thing that is typical in the area is raw sea urchin. I even had one straight from the sea after diving from the rocks. Just open it, and suck it up.

You've asked for the "easiest" way, so this may not be relevant, but if you're looking to save money you could check Skyscanner.com to see which airlines fly to Puglia from other European cities, then find an inexpensive flight from CA to one of those cities and go from there. We flew on Tuifly (not sure it even exists anymore) to Bari from Cologne-Bonn, Germany after flying into Frankfurt and taking the train to Bonn. We'd never been there, so we spent the night to see the town and went on the next day.

Hi Christine!
We were in Puglia in October and we flew from Milan to Brindisi. We spent on night in Brindisi and then took the train to Lecce - an easy one hour, inexpensive train ride. We loved Lecce - we picked up our rental in Lecce and drove around the region using it as a base for visiting Otranto, Leuca, and Gallipoli. We also spent two nights in Matera and two at Masseria Sant'Elia near Martina Franca. I'd be curious to know the name of the cooking class you're taking! You'll have a wonderful time in Puglia!