Kathryn Tomasetti tells us in Train travel in France: Carte blanche (Guardian, April 3) about her train hopping trips along the Riviera.
From June 1st to September 30th, a 24 hour rail pass, Carte Isabelle allows unlimited travel on any of the TER trains (no TGV) serving the 30 stations between Frejus and Ventimiglia for €12.
If you are looking for less touristy train routes by SNCF, Carte Isabelle also allows you to get aboard Train des Merveilles which runs in the back country from Nice to Tende.
From Tende, you can cross into Italy and reach Cuneo.
According to Train des Merveilles article on Provence Beyond, Nice to Tende is a two hour trip, add an extra hour for Cuneo.
They give us a sense of the adventure with following paragraph:
"The rail line follows the Peillon river valley north out of Nice, goes up the Roya Valley, and passes under the mountains at the Col de Tende into Italy. Much of the line is separate from the surface of the earth, either passing over it on numerous viaducts or passing through it in many, many tunnels, one of them about 6 km long between l'Escarène and Sospel."
From Cuneo you can continue on to Torino. That last leg takes around 90 minutes.
SNCF also offers a Family Option for Carte Isabelle for 4 people including 2 children 16 and under. You have the choice of daily option for 35€ or 3 consecutive days for 80€.
In all cases (individual or family), you can take unlimited rides on TER trains in Alpes-Maritimes and up to Frejus.
In the same spirit, SNCF offers Carte Bermuda which allows travelers unlimited TER rides between Marseille and Miramas on Saturdays, Sundays and Holidays (2nd Class only) for 5€ per person (adult or child) from July 1st to September 30th.
Marseille to Miramas via Port de Bouc follows the Cote Bleue.
For details on where to purchase Carte Isabelle and Carte Bermuda visit TER Provence-Alpes-Cotes d'Azur site (French only).
All this reminded me of my rides on Petit Train Jaune (Little Yellow Train) in Catalonia.
(* Photo of Train des Merveilles on viaduc du Faquin, between Peille and L'Escarène from Ma Ligne -French blog- by Armand Viale, the man in charge of Nice-Tende line)