actually, milan is not a very interesting city, the heart of milan is the area of duomo
- DUOMO is a must (the metro station name is duomo, so it is not difficult at all to find it)
but remember, DUOMO is a church and doesn't allow too sexy clothing
- then there is SCALA DI MILANO for opera fans
- SAN SIRO (ac milan and inter) for football lovers
- VIA MONTE NAPOLEONE and surroundings, you can find all luxury brands and enjoj a tax free of more than 10%
it is quite cold, not sure for rain, but sure is fog
but i don't think it is a problem for you, since you are studying in england
near duomo you fnd a lot of restaurants and bars, but they are very expensive, SPAGHETTI ALLA CARBONARA is a very good choice
then various PIZZA
PROSCIUTTO DI PARMA (recommeded as appetizer)
nothing special and very representative of milan that you can buy, except for gadget of the 2 football clubs of milan (ac milan and inter, as mentioned before)