If you find that renting a car is too expensive for your trip, then you can safely use Gallipoli's public transport system.
As elsewhere in Italy, there's a very tourist-friendly fare structure: a single ticket for a bus that is valid for 75 minutes from the time you punch it in costs 0.9 EUR. The same ticket but for a longer validity of 100 minutes will cost 1 EUR. During the validity period of a ticket, you can transfer several times. So you can conclude that transport in Gallipoli is quite affordable.
Please note that public transport tickets must be purchased at designated places in the bus stops. The ticket will cost 1.5€ directly from the driver so why should you buy your tickets in advance, why pay more?
For nightlife lovers, there is a special mode of transportation in Gallipoli. There are two buses that travel along the Ionian coast from Lido S. Giovanni to Otranto. Giovanni and Otranto (the port stop). They go all around Salento and the last stop is a noisy discotheque. The cost of such a trip is 5 EUR and includes a ticket to the disco.