The auspicious day of your arrival in Milan should be an easy one, I suggest holding off visiting the big sights today because you are not necessarily going to have the energy to appreciate them. Instead I recommend that you take the time to refresh yourself with a bout of shopping or perhaps an Aperitivo (the Milanese happy hour) and spa.
Shopping - If you have the money then I can suggest you nip to Via Montenapoleone or Via della Spiga for your high end shopping needs, But if you are watching your Euro Cents and want to be able to shop on a budget then take a leisurely stroll down Corso Buenos Aires. It is a long street so it might be advisable to catch the metro through some of it if you need. You can pair your shopping trip with a mini architectural tour as the strip is studded with some fantastic buildings and a rather large park for lunching in.
Aperitivo - Follow up your shopping trip with an aperitivo! The concept is essentially "after work drinks", the Milanese twist is that the venue will throw in a bountiful spread of nibbles to replace the dinner you won't be having by drinking. The food is free as long as you purchase a beverage and the venue will usually finish it all up at a sensible hour! Not only can it be quite a good night, but you get a free feed and have time afterwards to visit the spa! If this combination interests you, and why wouldn't it, I suggest you sample the aperitivo at "Friends" (10 Via Ludovico Muratori) or if you fancy the classic sit down meal, try the nearby "Casa Tua" (Corner of Via Ludovico Muratori and Via Bernardino Corio)
Spa - At the end of a long day, there is nothing more relaxing than a spa ...right?! Whilst researching things to do in this fair city I discovered QC Termemilano. It is essentially an inner city spa retreat (no funny business) in the heart of Milan. There is an amazing array of inclusions in your modest entry cost (€32-€59 depending on time of entry and extras) including saunas, steam rooms, relaxation rooms, aqua massage, pool, a wellness path and included buffet! Plus you get to walk around in a plush white robe and snazzy flip flops. This particular spa is quite close to my above mentioned aperitivos as well as the Porta Romana Metro stop.
Sightseeing ahoy! Today we meet some of historical Milan. Visit these sights in whichever order works best for you and spend as long or as short a time at each.
Duomo di Milano - This beautiful gothic cathedral is at the heart of Milan and is an absolute stunner! The exterior is an intimidating 65 metres high and opens up into a beautiful plaza full of pigeon feeders, tourists and rushed locals trying to get through to the other side as quickly as possible. (This is prime pickpocket territory so keep your valuables safe when taking your thousands of photos of this photogenic behemoth). If you have the energy I highly recommend you climb to the roof of the cathedral! It is open to the public and it gives you an amazing view over Milan, whilst getting you up close and personal with some of the 135 intricate spires and statues that make this building so beautiful.
Some of the stunning sights you will see if you climb to the roof of Duomo di Milano (known locally as Il Duomo).
Galleria Vittorio Emanuale II - The worlds oldest shopping mall is certainly a sight to behold! Behind it's grandiose entrance can be found the likes of Ferrari, Prada and Gucci as well as an array of overpriced eateries. Shop if you have the funds but, perhaps more interestingly, there is a beautiful mosaic at the crux of the cross shaped mall featuring four distinct crests. These crests represent the capitals of the four kingdoms of Italy; Milan, Rome, Florence and Turin. Legend has it that if you spin three times with your right heel on the testicles of the Turin bull then you will be bestowed good luck!
Teatro Alla Scala - When you stumble across this unassuming building, you would be forgiven for thinking it is nothing more than an uninteresting stock standard government building. Thankfully it is much more than it seems as it houses the stunning La Scala opera theatre! With €5 museum entry and an optional guide book in hand, you can feign aristocracy and peer across the stage from a luxurious booth or perhaps sip an imaginary flute of bubbly in the chandelier laden function areas. Whatever your chosen fantasy, La Scala is a great place to take a break from the hustle and bustle of Central Milan and absorb some theatre culture.
Panzerotti - Now since you are already in Central Milan, take a short stroll from the Piazza to the unassuming "Luini's". Here you will find a long deli cabinet stacked with a delicious array of pastry treats and just general deliciousness! The selection will have your mouth watering but I suggest you try the traditional Mozzarella e Pomodoro Panzerotti first for a traditional Milanese snack... Then go wild!
Castle Sforza - This castle museum almost seems more like an odd piazza than a traditional castle. The open hours vary from season to season but if you miss out on getting inside the building then don't be alarmed! The courtyard is always open and show cases some beautiful frescos and plenty of shade. The pockmarked exterior tells volumes about the castle's almost constant re-adaption based on who was ruling at the time. The castle does provide some amazing photo opportunities and the rust coloured interior walls really do remind you that you are in an ancient Italian city. An amazing place to wander, just mind the gypsies and stray cats.
Last supper - this is probably why you came to Milan, da Vinci's famed fresco on the refectory wall of the Convent of Santa Maria della Grazie Is certainly a talking point. Access to this artwork will cost about €8 and is timed so it is best if you book in advance and maybe base the sightseeing order of your day around this time slot. The experience is actually quite hilarious, due to the delicate nature of the fresco there can only ever be a certain amount of people in the room at one time for only a few minutes and there needs to be a small break between viewings to allow the moisture to be removed from the air. This means that you slowly plod through glass doors and vacuum seals like cattle in a science fiction slaughter house and then once in the room you get yelled at by an irate attendant over a loud speaker as though you are on "Big Brother". Possibly the most strictly archived piece of history in the entire of Italy! Oh and there is another fresco on the other side of the room too, just as good but not by Da Vinci.
I never advise booking in to see anything on your day of departure... Simply because Personally, I end up stressing about checking out, left luggage, missing my flight or not making it to the train in time! If you have a late night departure then I suggest you take some time to relax in one of the many restaurants, cafes and eateries that stud beautiful Milan or alternatively, the age old tradition of shopping always goes down a treat (and that spa is open all day too...)