Been to them all.
We visited Cassis and Nice, stayed a few nights in both places. Watched the 2012 WC game in Cassis on an iPad in the middle of the night. We thought about driving to Monaco for the day but decided against it and visited the town of Eze instead, which is a town on the top of a mountain.
Trains there are awesome but I would also recommend driving if you have the time and breaking up the trip. There is so much to see along the way -- small towns, wineries, parks, etc and driving there is a lot like driving here once you're outside of the cities. However if you were going to do the train, I would recommend at least one night in Lyon, it was my favorite city in France and it's the birthplace of cinema and French gastronomy. The bouchons there, basically small, family run bistros that serve amazing food, are famous. I ate at one and wish I had eaten at several more when we were there.
As for French Riviera -- Cassis is a nice small town, romantic, picturesque, etc...not sure if that's what this trip would be for you. Nice is a big city, probably my least favorite of the places we visited but it was still cool. It just didn't really blow me away...pretty touristy. The beaches are good but bring water shoes for sure. The pebbles are murder on your feet.
Florence was amazing...great city. Uffizi museum is the big dog there, but David is in a smaller musuem. We reserved a time in the afternoon when it's less crowded, I think it was like an hour before they closed. Go up in the duomo for cool views. Drink a lot of wine. Buy something leather. I'll try to rack my brain for some dinner suggestions but it's been 11 years now. Shit, I'm getting old.
I never had friends later on like the ones I had when I was twelve. Jesus, does anyone?