Arrive at Milano Centrale around 9:00 and use the station’s luggage lockers if you need to travel light; expect roughly €6–€10 depending on bag size and duration. Buy a 24-hour ATM ticket for about €7–€10 from the machines or ATM app—useful for the metro and trams all day. Take the M3 yellow line from Centrale FS to Duomo (about 10 minutes), then spend around 1½ hours at Duomo di Milano. The piazza and cathedral exterior are free, while a basic cathedral or rooftop ticket costs extra; for a €50 day, simply enjoying the square is perfectly worthwhile. From there, walk straight into Galleria Vittorio Emanuele II, where you can admire the glass roof, elegant shops, and the bull mosaic without spending anything.
Pick up a panzerotto at Luini, just behind the Galleria on Via Santa Radegonda. A classic costs approximately €4–€7; it is takeaway-style, so eat it outside in the nearby pedestrian streets rather than expecting a long sit-down meal. After lunch, walk back toward Duomo and take the M1 red line to Cairoli, or walk for about 15 minutes, reaching Castello Sforzesco for its free courtyards and exterior grounds. Allow about an hour, then continue through Parco Sempione toward Arco della Pace. This is the best part of the day to slow down: find a shaded bench, refill your water bottle at a public fountain, and enjoy the park before heading back toward Cairoli or Cordusio.
From Cairoli or Cordusio, take the M1 to Duomo, change to the M3, and return to Milano Centrale in roughly 20–25 minutes. Keep at least €10–€15 unspent for coffee, water, or an unexpected transport need; with free sightseeing, the transit pass, Luini, and optional luggage storage, you should remain comfortably within your €50 maximum.