There are many fantastic cycling routes around Nice that offer stunning views of the French Riviera and the surrounding mountains. Here are a few suggestions:

1. Col de Vence: This is a popular cycling route that starts in Nice and takes you through the hills to the Col de Vence, a mountain pass with an elevation gain of over 1,000 meters. The road is narrow and winding, but the views from the top are worth the effort.
2. Corniches: The Corniches are a series of three scenic roads that wind along the coast between Nice and Monaco. The roads offer stunning views of the Mediterranean and the cliffs that rise above it.
3. Col d’Eze: This is a classic climb that starts in Nice and takes you up to the hilltop village of Eze. The climb is steep and challenging, but the views from the top are spectacular.
4. Gorges du Loup: This route takes you through the Gorges du Loup, a narrow canyon with steep cliffs and a rushing river. The road is winding and challenging, but the scenery is breathtaking.
5. Col de Braus: This is another challenging climb that starts in Nice and takes you up to the Col de Braus, a mountain pass that offers stunning views of the surrounding mountains.
6. Mont Chauve: This is a lesser-known climb that starts in Nice and takes you up to the summit of Mont Chauve, a mountain that offers fantastic views of the French Riviera.