Menton

Many visitors to Nice note its Italian influences; but Menton, even further east and directly on the French/Italian border, is about as Italian as a place can get without actually being in Italy. From its dialect (which has Italian roots) to its name (which came from the Romans), Menton may be French by nationality, but its heart is all Italian.
This is especially true when considering its many gardens; after all, the Italian Liguria coast, which comes next after the French Riviera, is known as the “Riviera of Flowers,” and Menton fits right in. The Jardin Serre de la Madone, the Jardin botanique exotique de Menton and the gardens at Les Colombières villa are well worth a visitor's time – it's like a series of oases after city schlepping. 
Speaking of gardens, the symbol of the lemon can be found everywhere – and for good reason. It's the official symbol of the town, which grows the fruit as well as oranges. In fact, it's the Lemon Festival Capital of the World, with the party happening in February – a great off-season reason to visit this corner of the French Riviera. 

Practical Info

Menton is a half-hour local train ride from Nice and one stop away from Ventimiglia, the Italian border town.