Ciao UWT77

As a resident (since 2005), bits of Milan are ugly - agreed. But the historic centre is truly something...mostly beautiful and elegant. Simply passing the time people watching can be a pleasure.
Things to do...a clear day for the roof of the Duomo is hard to find, and I'd recommend doing the roof in any case. Hey, you might get lucky with the smog ;-) and in any case the gothic architecture of the cathedral as seen on the roof is worth the ascent (stairs or elevator - you choose). Make sure you go inside too and see the stautue depicting flailed skin.
Other things to do in Milan...if shopping (even just window) then head to the Quadrilato d'Oro (Golden Quadrangle) where the designers all have boutiques. The window displays can be pretty imaginative.
PP have mentioned the Basilicata di Sant'Ambrogio. Pretty good to look at and as the Patron Saint of Milan it'd be rude not to! And the Pinoteca di Brera.
If Modern Art is your thing, then there's a refurbished/new museum on via Palestro which could be worth a look. also check out what's on in Palazzo Reale (just off Piazza Duomo) as there is usually an exhibition of some kind on there.
For the Last Supper (Cenacolo) at the Santa Maria, if you don't book this about 3 months in advance then it's very difficult to get tickets...believe me I've tried for several visitors in advance and did not succeed on most occasions. But you can show up unannounced and ask about cancellations - does occasionally happen.
For a great (IMO) example of Fascist architecture, head to the Central Station at the northen end of Piazza della Reppublica - truly spectacular.
Nightlife-wise, plenty of restaurants around, and there's a Pizzeria on via Dante in the centre which is not bad. There are plenty of bars in and around town, and the Navigli area tends to be more bohemian than most. Trattoria Toscana is a nice restaurant on Corso di Porta Ticinese, with a good ambience.
You could take the metro (Line 1, Red) to QT8 and walk up the only hill in Milan...constructed from WW2 rubble I believe and gives a good view across the city too. Again on a good day you can see the Apennines and the Alps.
Getting out of Milan...you can take the train from stazione Cadorna to Como Lago Nord which is about an hour's journey. Como is worthwhile for a day but I wouldn't spend longer than that there.
You can also head to Bergamo from Stazione Centrale, again it takes about an hour. The main town is not all that special, but from the station you take the no. 1 bus towards Citta Alta and then the Funicular to the top. Citta Alta is "Old Bergamo" and really pretty. Good restaurants as alsways and pleasant to walk around. The air is noticibly clearer there and makes a welcome change from the smog which seems to be ever-present in the Po Valley these days. The price of being an industrial heartland!
Vencie is good too but I'd disagree with doing it in a day - on the fast train it's a 2hr45min journey each way and there's more to see than you can do in a day.

One more tip...if you (or someone you know) subscribes to The Economist, check out the City Guides section on their website - Milan is featured and has a Catch if You Can section every month.

Good luck!