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.
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.