The obvious answer: Sephora.
There are 115 Sephora store all over Italy, and mainly they are located in the bigger towns. Milan and Rome have 5 Sephora stores each, plus more stores located in malls just outside the city.
Sephora stores may vary for range of brands they carry and for range for brand.
There are a few huge stores that have the full line of many brands and also houses the boutique section for Make Up For Ever and Benefit (the store in via Vittorio Emanuele in Milan is one of those store).
The other stores are usually medium sized and have a selection of brands and product.
You will always find the main luxury brands, such as Armani, Dior, etc but also MUFE, etc.
Many store won't have products from the smaller international and national brands.
Many Sephora are currently being equipped with the famed Benefit brow bars.
It's worth noting that Sephora has a loyalty card, which is free and comes with many perks. The first time you'll step in an Italian Sephora, at the register they'll ask if you have the Sephora Card. If you don't, they'll offer one on the spot. It's a white card that will be swiped for your first purchase and then you are supposed to activate online. Sometime they give you a small discount with your first purchase. This white card is a temporary card and once you are registered and you used your white card 4 times, you'll receive at the address you gave a black card and your first 10% off coupon. This card will have your name on it and its number will be linked to your online profile so online purchases are counted toward the rewards.
Let's talk about the rewards of the Sephora program.
Every 4 times you swipe your card or 150 points (1 point = 1€) you get a 10% off. It's not applied automatically to your next purchase, you are supposed to ask when you are at the register. Only one card swipe per day is counted toward the discount. You can spend 1€ or 10€, it doesn't matter: you will receive a 10% off once you have 150 or 4 card swipes. This is the basic discount.
Every now and then, Sephora will award a 15% or 20%, and this happen when you haven't purchased anything for a time or in special occasions (i.e. St. Valentine's, Christmas, etc.). These discounts can be linked also to particular events in a particular Sephora store or valid for just one brand, so be careful to read the fine print. They also expire, so pay attention to what's written on the coupon (which will be mailed, texted, or emailed to you).
The Sephora Black card also gives you access to particular events or products ahead of the general public, and you'll be given a small gift on your birthday.
If you get to 1000 point in one year, you get the Sephora Gold card, which means an automatic 10% off every purchase, a really nice gift on your birthday and on special occasions, free access to the Beauty bars and private costumer service.
Unfortunately cards from outside-Italy Sephora stores are not valid in Italy, and vice versa: your Italian Sephora card will not work outside Italy.
I highly recommend getting a Sephora card if you are planning to stay in Italy for a while and are a beauty addict!