The distance from Nice airport to Menton is about 30 km. It can be traveled in three ways.
The most comfortable, but at the same time the most expensive option is a cab. Unofficial carriers are not allowed on the territory of the airport. State cabs come to the terminal exits in the order of the live queue. Drivers are very courteous, help to load luggage, and make sure to turn on the meter. The cost of a cab ride from Nice airport to Menton is 85-95 EUR during the day and 105-115 EUR at night. For up-to-date fares see here.
The second option is a bus. Direct express bus #110 runs daily from 8:45 to 21:15 (departing from platform #2). The ticket price for an adult is 20 EUR, for a child under 12 years old - 12 EUR. For the fourth and each subsequent suitcase you will have to pay 5 EUR extra. Travel time is approximately one and a half hours.
If you arrive at night, take the night bus #100, which runs from 22:00 to 2:30. It also departs from platform 2.
Finally, you can reach Menton by train, which departs from Nice St Augustine station in Nice. You can walk to it from the airport in 15-20 minutes or take one of the many shuttle buses. Tickets for the train cost 5 EUR. Travel time is 30-35 minutes.