We have not been to Gallipoli, so I cannot address that one. We did go to Otranto with our Road Scholar group, but all we saw there was the Tree of Life floor mosaic in the church. It is wonderful. We learned a lot from our guide about the history of the town, including the devastating attack by the Ottomans in 1480. But we did not see much of the town itself; or if we did, it was not particularly memorable.
We did visit Monopoli on our own, on a daytrip from Lecce. We took the train up, walked abound and were charmed by the lovely oldtown area with its white buildings (many with blue doors, as I have seen in photos of some Greek Islands). We stopped for lunch at a restaurant with outside tables and enjoyed a fresh seafood salad (skipping the fresh-caught sea urchins we saw a fisherman drop off in a bucket 5 minutes earlier). And then we wandered along the seafront to a sandy beach I identified on google satellite view. And my husband went for a swim in the Adriatic. That was exactly a year ago today—-February 24, 2023. I just remembered that when I saw your post and thought of Monopoli.
So you can probably guess which would be my Number 1 recommendation. I will leave it to others to help you decide on the second.