Menton to Nice Provence

By train, about 35 minutes; by bus, about an hour (subject, of course to traffic). The bus costs €1 (day pass is €4 and 7 day pass is €15), and the train costs €4.90. The train is twice an hour, and runs later than the bus; the bus is every 15 minutes. Which is better? Both are fine, so it's your choice (price vs speed and comfort). If you are taking a late train, be sure to have a round trip ticket or coins. I don't know about Menton station, but Monaco station was unstaffed in the evening, and there was no way to buy tickets without coins (the machines didn't take paper money or US-issued credit or debit cards). Train information: http://www.tgv-europe.com/en
Bus information: http://www.lignesdazur.com/index.asp

Thank you very much!

The bus goes by the middle corniche, which means a spectacular view down to the ocean (from seats on the left-hand side of the bus as going from Menton to Nice). To me, the bus station in Nice is marginally more centrally located than the train station. Either one is fine!