If you are in for an afternoon/evening, you could spend some of the time in the Duomo/Quadrilateral area; there is the famous Church and a bunch of museums nearby, along with the Galleria and the fashion shops (Via Montenapoleone/Via della Spiga) etc.

Then I might head over to the Navigli for an aperitivo (there is a separate thread below) and dinner would depend on what you like to eat (traditional Lombard food or something else) and your price range.

The best place to stay would be a hotel somewhat near some of these things, either in the city Center or nearby. As you are SPG Plat, you could see the thread in that forum to see what people think of the Gallia, Westin, Diana and Four Points, all of which are relatively well situated but substantially different in price/experience.