Amazed nobody mentioned Torino (Turin)! Just a few hours by train (or bus) from Nice this is a simply sensational place and, probably the most under-estimated city destination in Europe based on what I saw of it a few years back. I travelled in the other direction (Torino to Nice), the train passing through the small towns of Northwest Italy, Cuneo, Mondovi, etc. and the stunning mountain scenery and towns and villages on the French side in the "arriere-pays" of the Provence alps behind Nice. One train per day is designated a "tourist train" probably because it goes a bit slower to admire the scenery and stops ar more places you might want to stop at.
Torino itself is FULL of galleries, museems, castles, palaces, churches, piazzas, art-deco cafes and railway stations like cathedrals. I think I heard that the famous "Shroud of Turin" is on exhibit this year, which it normally is not - but even without the shroud, the city has everything - stunning architecture, restaurants and bookshops everywhere, romantic eateries along the river Po at night, the huge "Mole" tower and its gawping views of the city and the snow capped mountains that encircle it, students sketching by the river, people eager to welcome you, altogether a truly beautiful city. Much of the centre of Nice's own Italianate architecture (around Place Masena) is copied from the style of Turin, which reflects the close link and bond that existed between the two cities when Nice was still part of Italy, the same route linking them across the mountains today as was the case back then.
Of course Italy has great and deservedly well known cities such as Rome and Florence and Venice as well as a dozen others anyone can name - but Torino is unquestionably the country's best kept secret. And, so easy to get to from Nice. As well as the mountain train (which is the most interesting way to go), it is also possible to travel less scenically by the (more frequent) trains VIA Ventimiglia/Genoa connecting northward for Torino. On my trip I had to partially resort to this route having spent a few days at Breil-sur-Roya during which one of France's infamous rail strikes had raised its head.
kb