Brindisi Airport (Salento): This is the sensible airport: rent a car at the airport and drive to Cisternino in roughly 50–60 minutes. Public transport is possible but not elegant: airport bus to Brindisi Centrale, then regional/Ferrovie del Sud Est connections via Francavilla Fontana toward Cisternino Città; allow about 2 hours or more and roughly €8–15, with schedules worth checking before you commit. A pre-booked transfer is preferable to an airport taxi if you are not driving.
Bari Karol Wojtyła Airport: Choose Bari only if the flight is substantially better. A rental car takes about 1 hour 15 minutes to 1 hour 30 minutes. Without one, take the airport rail link to Bari Centrale, then Ferrovie del Sud Est services toward Martina Franca/Cisternino Città; it is usually a 2½–3½-hour, multiple-leg trip for around €10–15. Do not confuse an inexpensive fare with a convenient transfer.
Bari Centrale: The practical long-distance rail gateway. From the station, use Ferrovie del Sud Est toward Martina Franca and onward to Cisternino Città; expect a change and roughly 2–3 hours total, depending on the connection. Buy/check FSE tickets and timetables on the operator’s own site: these services may be poorly represented in general journey planners.
Brindisi Centrale: Useful if arriving on the Adriatic main line, but not a simple rail hop: continue by regional/FSE services, generally via Francavilla Fontana, and allow around 1½–2½ hours. If there are two or more people, a pre-arranged car transfer can be worth the premium over losing half a day to sparse connections.