We are thinking about a visit to Genoa and possibly Santa Margherita Ligure... Will it be difficult to find train transportation between Menton, France and either Genoa or Santa Margherita Liguere?
Ventimiglia Italy is just across the border from Menton. Frequent trains connect France to Ventimiglia where you can catch trains to Genoa and further on along the coast. This is a heavily traveled route, with train changes often in Ventimiglia and Genoa.
We took the train between Villefranche sur Mer, a great town just east of Monaco, to a fav of ours, Santa Margherita Ligure. Easy, just bought the tickets when we arrived in Villefranche. Funny though as the French crew had to wait for the Italian crew at the border and they were quite annoyed with "Italians"