What sort of nightlife are you looking for?
My sons are young adults. So they are looking at lively bars with music and ambiance.
OK. Look far from my level of expertise but from driving through fairly often, the area around Piazza Mario Cortesini strikes me as being a lively place. Even one Sunday afternoon when we merely stopped for a cup of tea, the bar we were sitting outside was playing very loud music so it's possibly quite lively at night. They could start with there.