lV, Prada, Gucci in Milan and Rome. Some unique designer items are only available in Milan. Go the shopping mall to the left of the Duomo and go up to the second floor, you will feel like you are in designer heaven, with Gucci, Tods, MCM, Prada, et al. all right next to each other and downstairs the individual stores. Have fun! In Rome, I found great stuff on Via Veneto and Via Condotti. Many, many designer shops and I feel that they were cheaper.
If you go to Milan, be sure to take a day trip to Foxtown outlet in Switzerland. The bargains were excellent and it's only about 1 hour by bus to get there. They had Prada, Gucci, Valentino and other designer outlets.
Definitely visit Seravelle designer outlets, about 1.5 hours from Milan. All the premium brands are there, with the exception of Tods, I think. I have gotten items from Prada and Ferragamo several times, all great bargains!