Note that http://www.trenitalia.com/tcom-en is currently only showing trains on this route until June 9, though times are likely to be the same or similar afterwards.
Also, http://www.trenitalia.com/tcom-en only sells tickets for this route on conections using the Thello trains from Nice-Ville to Savona. For connections requiring a change at Ventimiglia, buy Nice-Ventimiglia in Nice and the rest from Trenitalia online or in Ventimiglia.
Many people would prefer to do this journey all or partly by car rather than by train - it'd be faster, and a car is very useful for touring in the Bra-Alba area. If returning the car to Nice, rent in Nice. If not, to avoid the massive cross-border drop-off fee you can rent from Hertz in San Remo or at Alassio train station, and from all major rental companies in Savona. Except on Sundays.