Then straight to Peterborough the day after?! There's a few shed bars around and loads of pop ups selling club tat but not much to do really other than just walk around staring up at the incredible structure of the stadium. Metro from centre of Milan is quick and cheap at least.
Its a proper, proper dive inside the ground and I'd have a piss outside rather than brave those urinals but it's an amazing experience and one of football's must see places. If you're on the front few rows of one of the tiers and Milan score you get to pile forward to the barriers with everyone celebrating, it's ace.
You should absolutely aim to go for a night out in the Navigli area, loads of interesting bars and restaurants lining the canals. Puts the myth about Milan having no nightlife to bed.