i go to Milan regularly – it has 3 airports, only one of them is in Milan! the logistics of just staying the night and catching the train to florence wont be that simple… actually i think London city fly into Linate which is the closest to the city anyway!
didnt rate Florence myself, nothing there that isnt in the guide books! not like Rome, Rome has all the guide book shiz but behind that is a really cool and vibrant city. florence has nothing going on and neither does Milan actually unless you like shopping!
if it was me id fly into Milan, rent a car and have tour round the lakes, Varese, Como, Lugano… Bergamo is nice too.