I agree that TLN (Toulon-Hyères airport just south east of Hyères) is a convenient airport to fly into if you're interested in visiting St Tropez.
TLN is relatively small, but well supplied in low-cost and regular carriers. Nice & Marseille are both larger. Most folks looking visit Provence go to Marseille, those more interested in greater Nice area fly into Nice.
From Nice, you can take a bus to the train station, train to St Raphael then bus or boat to St Tropez. Not hugely convenient especially with connections, but doable.
From TLN, you take a 10min shuttle bus into the town of Hyères to stop at their Gare Routière. From there, SODETRAV bus 103 takes you to St Tropez in about 1hr30mins. You pay for the fare on the bus.
For the Hyères to St Tropez bus schedule, check out sodetrav.fr -> Horaires -> and look at the "Lignes InterUrbaines" schedule for bus 103 for your visit month/day.