Check in and drop luggage (many hotels allow luggage drop if early). Breakfast at a nearby café — try Sant'Eustachio Il Caffè (opens ~7:30am) for classic Roman coffee and cornetto.
Enter St Peter's Basilica (usually open 7:00am–7:00pm) to see the Papal Holy Door and the basilica's interior — climb the dome if you like (extra cost, opens ~8:00am).
Visit Milan Cathedral (Duomo) and take the rooftop walk for city views (Duomo open roughly 9:00am–7:00pm; rooftop hours vary). Pre-book timed entry to avoid queues.