This is completely up to you! You can go to the beach, or go explore the city. All we ask is that you show up to the ceremony on time :)
We loved our time in Gallipoli and would recommend it if you're looking to spend more time in Puglia. It is 30 mins from Lecce and has some amazing beaches (Punta della Suina was our favourite).
On our trip in 2023 we did 1 night in Gallipoli, 2 nights in Otranto, 2 nights in Ostuni and 1 night in Monopoli
I swear by the blog "Along Dusty Roads" and used it to plan our entire Puglia trip, but they have guides for various destinations in Europe. https://www.alongdustyroads.com/everywhere