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You can follow the path around Cap de Nice half way to Villefranche, but be prepared for several hundred steps up to rejoin the road. It’s a very beautiful walk and you will find mostly local people using it.
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The castle hill overlooking the Baie des Anges and harbour offers a spectacular vantage point overlooking the city. Not much is left of its ruined castle besides crumbling walls. Still, climbing up the stairs to reach the platforms 90 m above Nice is well worth the view. There is also a lift (ascenseur) which will take you three quarters of the way up. The castle hill park closes at around sunset. Expect to be escorted outside if you stay longer.
Even if you are not in art, this is a museum which should not be missed. It includes stained glass windows by the artist.
Charming collection of paintings, drawings and sculptures in 17th-century Genoese villa.
The ruins of the Gallo-Roman settlement in Cimiez, plus a museum with nice documentation on Gallo-Roman life (but mostly not in English). Activities for children. Guided tours available.
To the west, there is the Musée des Beaux-Arts, housing an excellent collection of pastels and other works by Jules Cheret, among other artists.
2500 different plants in botanical garden and tropical glass house. Also various animals.