From Nice, Ventimiglia can be reached by the SNCF (the french railway company) train that also passes through Monaco. The adult fare from Nice is € 6.40 for adults / € 4.80 for youth (12-25 years) (as of August 2010). To purchase tickets here, you will need the amount in coins or an EC/Maestro debit card. Be aware that in Ventimiglia, the ticket automats are often out of service.
The "new" town center and shoreline are an easy walk toward the south from the terminal. The original/historic section is across the river to the west...also an easy walk