Well, I would say, that to begin with, this is the most beautiful part of the world:
201260201 by
mfogiel, on Flickr
Photographically speaking, there are many picturesque places to visit, and the most interesting is certainly Monaco:
MF20100412 by
mfogiel, on Flickr
Above Monaco. you have a nice village with a stunning eagle's view, La Turbie , and a distinct historical imprint of the Roman domination over the entire area, Le Trophee d'Auguste:
MF20101206 by
mfogiel, on Flick
Menton, is the last seafrony town before Italy - bordering Ventimiglia.
Menton ( Cocteau Museum):
20120604 by
mfogiel, on Flickr
Ventimiglia (old):
20093618 by
mfogiel, on Flickr
On the other side of Nice (direction Marseille) you can find many interesting hilltop villages, like the above mentioned Mougins, St. Paul de Vence, Vence, and along the sea Antibes, Cannes and St Tropez, but the seafront gets progressively flatter. In My opinion the best part is between Nice and Menton.
Vence:
20093234 by
mfogiel, on Flickr
Mougins:
20102604 by
mfogiel, on Flickr
St Tropez:
20104022 by
mfogiel, on Flickr
Finally, Nice is very attractive, with the Promenade des Anglais, old town and Massena square, always full of life.
Promenade des Anglais:
20112911 by
mfogiel, on Flickr
Enjoy your trip !