I'm actually not a big fan of Nice or the French Riviera, but if you have time, definitely do the drive along the coast. I like Monte Carlo best, and you can take the helicopter from Nice airport as ajinlondon said. It's been a few year, but the price sounds about right. The area is relatively safe... if you feel comfortable in Rome, you'll have no problems here.

As for Rome versus Milan, I'd always go for the former, but then again, I tend to be in Milan a lot for work. If you go there, try if it all possible to fly to LIN instead of MXP. You could try something different too... how about Florence? A beautiful city with lots of sights and fantastic countryside. If you have the time, drive from Florence to Siena and spend some time enjoying the wines (after driving, obviously ).

Or how about some Austro-Hungarian charm? BUD is a great place to spend a day or two, and you get more miles than to FCO.