In Brindisi flights landing many low-cost.

Train, you can drive to Lecce and then change to the 'sud-est' line and go Alessano. This small train is a Pearl of Salento, with which you can explore other small towns.

The car is of course always the most convenient, as must the public funds not so often and not get too. If you're without a car, can rent one in Alessano, and also scooters or bikes.