I myself do not think for a moment this well has anything to do with St. Paul, apart from the fact that it was found in a city where he dwelt. But it seems to be a major attraction, so here are some pictures (from two visits).
What you see is: a well. Next to it a glass-covered excavation of some Roman foundations. A number of columns of (to my knowledge) unexplained origin, and some adornment.
The spot is a good starting point for a walk in the neighbourhood with some fine old houses, some well-restored.