@geekman as this was an old haunt of his
It was indeed, lived there for a couple of years and know most of the Riviera / Northern Italy.
Most places are easy to get to by train and there's a fairly good bus service too.
Eze is nice, skip the perfurmerie as it's a tourist trap, if you want to drive a supercar for a while go to the perfumerie carpark and there's normally a stand there where you can rent them. It's not cheap but good fun and you can drive them on both the Moyenne and Grande Corniche. When I was working there I used to let people drive the cars as they were supposed to be driven, hopefully whoever took over from me does too.
There's a beautiful hotel in Eze called the Chevre D'or where you can have a drink, you get a nice view.
You should definitely go to La Turbie and walk to La Tête de Chien which provides an amazing view of Monaco. The backstreets of the old town of La Turbie are really nice as well, and the bakery is decent for lunch.
Nice itself is a nice town with good nightlife, there used to be a bar at the start of the Promenade Des Anglais which served massive jugs of mojitos which was good fun, can't really go wrong walking along the promenade / beach etc.
For Monaco, go to Casino Square, walk behind the casino to the right as you're facing it and you can enter a free garden where you get a nice view of the sea and the city. Obviously, food and drink in Monaco are expensive, if you don't want to spend a lot I recommend Bar de L'Oliveraie, it's a bit out of the central district and is relatively cheap, nothing fancy but fine for a quick lunch.
Ventimiglia is nice, but when I lived near there they were having a lot of issues with illegal migrants, there were quite a lot of fights between them and the locals and generally a bit of a tense atmosphere. I'm not sure how it is right now. It's a fair bit cheaper than the Cote D'Azur and a nice place to have food / drink, I recommend Osteria Consani.
Menton is also really nice, both the old town and the beach area are really nice to walk around, lots of nice restaurants.
If you have any questions let me know.