Archaeologists consider San Giovanni alle Fonti most likely the baptistery Ambrose used, which is a historical judgment, not a Church definition. It is an excavation, with no chapel furnishings, and most people around you will be sightseeing; treat it as a place of prayer all the same.
The baptistery is not part of the basic cathedral visit. Under the cathedral's access rules in force since April 1, 2025, the most recent it has published and read for this answer on October 10, 2026, the archaeological area with the baptistery is a 5-euro ticket that must be held together with a cathedral ticket, and it is included in the Culture Pass at 15 euros (13 reduced), valid for two days. The ticket offices beside the cathedral are open daily from morning until early evening, with the last ticket sold shortly before closing. The cathedral sometimes suspends visits for liturgies, so look at its notices on the day.
Other places complete the story. St. Ambrose himself is buried across town in the Basilica of Sant'Ambrogio, a short metro ride away. Cassago Brianza, north of Milan, is commonly identified with Cassiciacum, where Augustine prepared for baptism, though other locations have been proposed. Pavia holds his relics. Ostia is where his mother, St. Monica, died later in 387, and her relics now rest in the Basilica of Sant'Agostino in Rome.