Train is probably best as they are excellent in that part of the world. See this link for details http://www.ehow.com/how_2029728_train-nice-milan.html almost 8 years ago
Train is a fantastic way to see more of southern France and the Liguria region of Italy. The train from Nice will take you through along the beautiful southern coast (including Monaco/Monte Carlo), crossing over the border to Italy (the first stop in Italy is Ventimiglia). The train from Ventimiglia then carries along the Italian coast of seaside resorts to Genoa. You can then go to Genoa direct to Milan. Flying from Nice to Milan will involve a stop, depending on which airline eg. via Zurich with Swissair.
I've done this journey (the other way) and can really recommend it if you have time. If you need any more help with your trip, let me know - it's what I do :) almost 8 years ago